Yes (at least some of them).
I've done a thorough trawl through the books, including Fantastic Beasts and Where to Find Them, in search of all the plants and animals which Lovegood believes in. I've tried my best to make the answer exhaustive. Some of the plants and animals are only mentioned in passing so it's not possible to be definitive on whether or not they exist. I've included entries which are mentioned by Luna Lovegood too since she often touts the beliefs of her father. I've also included creatures and objects referenced in The Quibbler.
My conclusion: not everything Lovegood believes in is nonsense, although some of it is. At least six things mentioned by Xenophilius Lovegood definitely exist.
The question seems to be looking for things which Lovegood believes is real but nobody else does. Naturally, these examples are much harder to find. I've evaluated in each instance whether it's likely that the creature or plant is real, and whether its existence is taken seriously by the public at large.
Things which actually exist and which are also believed to exist by others.
Goblins
Lovegood mentions goblins in The Quibbler.
"Cornelius 'Goblin-Crusher' Fudge, that's what his friends call him. If you could hear him talking when he thinks no-one's listening, oh, he's always talking about the goblins he's had done in."
(Order of the Phoenix, Chapter 10, Luna Lovegood).
We see plenty of goblins elsewhere in the series. They are a widely believed in throughout the wizarding world.
Kumquats
Also from The Quibbler:
According to the magazine, if you turned the runes on their heads they revealed a spell to make your enemy's ears turn into kumquats.
(Order of the Phoenix, Chapter 10, Luna Lovegood).
Kumquats are normal fruits found in the Muggle world, so presumably were widely believed in by wizards.
Garden gnomes
Xenophilius believes in these.
"[Luna] lingered in that charming little garden to say hello to the gnomes, such a glorious infestation. Few wizards realise just how much we can learn from the wise little gnomes - or, to give them their correct name, the Gernumbli gardensi."
(Deathly Hallows, Chapter 8, The Wedding).
We see the Weasleys' garden gnomes on several occasions so they're definitely real. They also appear in a Gilderoy Lockhart book, so were presumably widely accepted by the public.
"Now, let's see what Lockhart's got to say on the subject."
[...]
Harry looked at the cover of Mrs Weasley's book. Written across it in fancy gold letters were the words: Gilderoy Lockhart's Guide to Household Pests.
(Chamber of Secrets, Chapter 3, The Burrow).
Although his beliefs in the magical properties of gnome saliva may not be scientifically verified.
[Luna] held up her finger and said, "Daddy, look - one of the gnomes actually bit me!"
"How wonderful! Gnome saliva is enormously beneficial!" said Mr Lovegood, seizing Luna's outstretched finger and examining the bleeding puncture marks. "Luna, my love, if you should feel any burgeoning talent today - perhaps an unexpected urge to sing opera or to declaim in Mermish - do not repress it! You have been gifted by the Gernumblies!
(Deathly Hallows, Chapter 8, The Wedding).
Mistletoe
Lovegood has a sign outside his house which references mistletoe.
Pick Your Own Mistletoe.
(Deathly Hallows, Chapter 20, Xenophilius Lovegood).
Harry observes this himself.
Two aged crab-trees, bent with the wind, stripped of leaves but still heavy with berry-sized red fruits and bushy crowns of white-beaded mistletoe, stood sentinel on either side of the front door.
(Deathly Hallows, Chapter 20, Xenophilius Lovegood).
Mistletoe is a pretty standard thing, accepted by everyone. Cho Chang expressed no scepticism in it, especially when Harry was standing underneath it.
Freshwater Plimpies
Xenophilius says that Luna is fishing for plimpies in a nearby stream.
"Where's Luna?" asked Hermione. "Let's see what she thinks."
Xenophilius gulped. He seemed to be steeling himself. Finally he said, in a shaky voice difficult to hear over the noise of the printing press, "Luna is down at the stream, fishing for Freshwater Plimpies. She...she will like to see you."
(Deathly Hallows, Chapter 20, Xenophilius Lovegood).
The plimpy is a real animal, cited in Fantastic Beasts and Where to Find Them.
Plimpy
M.O.M. Classification: XXX
The Plimpy is a spherical, mottled fish distinguished by its two long legs ending in webbed feet. It inhabits deep lakes where it will prowl the bottom in search of food, preferring water snails. The Plimpy is not particularly dangerous, though it will nibble the feet and clothing of swimmers. It is considered a pest by merpeople, who deal with it by tying its rubbery legs in a knot; the Plimpy then drifts away, unable to steer, and cannot return until it has untied itself, which may take hours.
(Fantastic Beasts and Where to Find Them).
It's not totally clear whether the plimpies Lovegood refers to are the same ones which feature in Fantastic Beasts. Those plimpies are said to live in "deep lakes", which doesn't quite fit with the stream-dwelling plimpies Lovegood describes. It's certainly not inconceivable that there may be different varieties of plimpy which suit different locales, however. We should also factor into the equation the fact that Lovegood was bluffing at this point about where Luna was. So he may not even believe in Freshwater Plimpies. However, lies are more effective when based on reality so I suspect that Lovegood may have been referencing real creatures here.
Presumably the wizarding world would accept the legitimacy of the creatures found within Fantastic Beasts and Where to Find Them as the book is widely respected.
Newt’s masterpiece has been an approved textbook at Hogwarts School of Witchcraft and Wizardry ever since its publication and must take a substantial amount of credit for our students’ consistently high results in Care of Magical Creatures examinations – yet it is not a book to be confined to the classroom. No wizarding household is complete without a copy of Fantastic Beasts, well thumbed by the generations who have riffled its pages in search of the best way to rid the lawn of Horklumps, interpret the mournful cries of the Augurey, or cure their pet Puffskein of drinking out of the toilet.
(Fantastic Beasts and Where to Find Them).
Billywigs
Lovegood speaks of a Billywig as being a constituent part of his model of Rowena Ravenclaw's diadem.
He indicated the objects like ear-trumpets.
"These are the Wrackspurt siphons - to remove all sources of distraction from the thinker's immediate area. Here," he pointed out the tiny wings, "a Billywig propeller, to produce an elevated frame of mind."
(Deathly Hallows, Chapter 20, Xenophilius Lovegood).
Similarly, this creature has been verified to be real by Newt Scamander and features in Fantastic Beasts:
Billywig
M.O.M. Classification: XXX
The Billywig is an insect native to Australia. It is around half an inch long and a vivid sapphire blue, although its speed is such that it is rarely noticed by Muggles and often not by wizards until they have been stung. The Billywig’s
wings are attached to the top of its head and are rotated very fast so that it spins as it flies. At the bottom of the body is a long thin sting. Those who have been stung by a Billywig suffer giddiness followed by levitation. Generations of young Australian witches and wizards have attempted to catch Billywigs and provoke them into stinging in order to enjoy these side effects, though too many stings may
cause the victim to hover uncontrollably for days on end, and where there is a severe allergic reaction, permanent floating may ensue. Dried Billywig stings are used in several potions and are believed to be a component in the popular sweet Fizzing Whizbees.
(Fantastic Beasts and Where to Find Them).
Borderline cases.
Dirigible Plums
The Dirigible Plum exists and, again, features on Lovegood's replication of Ravenclaw's diadem.
"Finally," he pointed to the orange radish, "the Dirigible Plum, so as to enhance the ability to accept the extraordinary."
(Deathly Hallows, Chapter 20, Xenophilius Lovegood).
Clearly the plums are not figments of Lovegood's imagination. There is something real which Lovegood refers to as a Dirigible Plum and which he grows in his garden. Luna also wears them as earrings. Whether the rest of the wizarding community is aware of the Dirigible Plums or refers to them as such is unclear, as the Lovegoods are the only ones who ever refer to them.
Gurdyroots
Again, something definitely exists in the real world which is referred to by Luna and Xenophilius as a Gurdyroot.
[Luna] thrust what appeared to be a green onion, a large spotted toadstool and a considerable amount of what looked like cat litter into Ron's hands, finally pulling out a rather grubby scroll of parchment that she handed to Harry.
[...]
"What's this, by the way?" [Ron] added, holding the onionlike object up to eye-level.
"Oh, it's a Gurdyroot," she said, stuffing the cat litter and the toadstool back into her bag.
(Half-Blood Prince, Chapter 20, Lord Voldemort's Request).
Xenophilius Lovegood also serves the trio an infusion of Gurdyroots.
Again, the Gurdyroot is real. It's not entirely clear whether others believe in it too. It's possible that the Gurdyroot was sold as an amulet to ward off the Monster of Slytherin. Although it's not named, one of the items Neville buys seems to match the description.
Meanwhile, hidden from the teachers, a roaring trade in talismans, amulets and other protective devices was sweeping the school. Neville Longbottom bought a large, evil-smelling green onion, a pointed purple crystal and a rotting newt-tail before the other Gryffindor boys pointed out that he was in no danger...
(Chamber of Secrets, Chapter 11, The Dueling Club).
If it was a Gurdyroot which Neville bought then that may go some way towards legitimising the Gurdyroot as 'real', not just for the Lovegoods but for everybody else.
Things which actually existed, but which others didn't believe in.
There are no clearcut examples, although Gurdyroots and Dirigible Plums may count.
Things which didn't exist, which the Lovegoods didn't believe in but which others did.
None! If the Lovegoods don't believe in it it doesn't exist! Dabberblimps are video game canon so are included in this category.
Things which didn't exist, which were believed in by the Lovegoods but not by others.
Crumple-Horned Snorkacks
The humble Crumple-Horned Snorkack does not exist, despite the insistence of Xenophilius. Nobody else seems to have even considered that they may exist.
Blibbering Humdingers
These are mentioned by Luna and confirmed as non-existent by Hermione.
"You can laugh," Luna said, her voice rising, apparently under the impression that Parvati and Lavender were laughing at what she had said rather than what she was wearing, "but people used to believe there were no such things as the Blibbering Humdinger or the Crumple-Horned Snorkack!"
"Well, they were right, weren't they?" said Hermione impatiently. "There weren't any such things as the Blibbering Humdinger or the Crumple-Horned Snorkack."
(Order of the Phoenix, Chapter 13, Detention with Dolores).
This is the only reference to this creature in the books. I think we can depend on Hermione to speak the truth here. She's abnormally well-informed on such topics and can be presumed to speak for her fellow-wizards and -witches when she says that Humdingers do not exist.
Heliopaths
Heliopaths are described by Luna.
Nearly everyone looked stunned at this news; everyone except Luna Lovegood, who piped up, "Well, that makes sense. After all, Cornelius Fudge has got his own private army.
"What?" said Harry, completely thrown by this unexpected piece of information.
"Yes, he's got an army of Heliopaths," said Luna solemnly.
"No, he hasn't," snapped Hermione.
"Yes, he has," said Luna.
"What are Heliopaths?" asked Neville, looking blank.
"They're spirits of fire," said Luna, her protuberant eyes widening so that she looked madder than ever, "great tall flaming creatures that gallop across the ground burning everything in front of -"
"They don't exist, Neville," said Hermione tartly.
"Oh, yes, they do!" said Luna angrily.
"I'm sorry, but where's the proof of that?" snapped Hermione.
"There are plenty of eyewitness accounts. Just because you're so narrow-minded you need to have everything shoved under your nose before you -"
(Order of the Phoenix, Chapter 16, In the Hog's Head).
Make what you will from that exchange. Personally, I am in little doubt that the reader is meant to believe Hermione, although it's interesting that Luna seemingly has eyewitnesses who can testify to the existence of the Heliopaths. It's more than likely that they did not exist, and that the wider public didn't believe in them (especially as they are apparently Cornelius Fudge's private servants, a favourite point of intrigue for The Quibbler). The description of Heliopaths is not altogether dissimilar to the effects of Fiendfyre, although presumably Luna is not getting confused between the two.
Wrackspurts
The Wrackspurt is another creature which seems likely to be a part of the Lovegoods' imagination. When Harry is lost in thought about being the Chosen One...
"You all right, Harry? You look funny," said Neville.
Harry started.
"Sorry - I -"
"Wrackspurt got you?" asked Luna sympathetically, peering at Harry through her enormous coloured spectacles.
"I - what?"
"A Wrackspurt...they're invisible, they float in through your ears and make your brain go fuzzy," she said. "I thought I felt one zooming around in here."
She flapped her hands at thin air, as though beating off large invisible moths. Harry and Neville caught each other's eye and hastily began to talk of Quidditch.
(Half-Blood Prince, Chapter 7, The Slug Club).
Harry and Neville certainly seem to find the concept of the Wrackspurt ridiculous, as did Victor Krum.
"That's her," he said, pointing at Luna, who was still dancing alone, waving her arms around her head like someone attempting to beat off midges.
"Vy is she doing that?" asked Krum.
"Probably trying to get rid of a Wrackspurt," said Harry, who recognised the symptoms.
Krum did not seem to know whether or not Harry was making fun of him.
(Deathly Hallows, Chapter 8, The Wedding).
I think that this is enough to conclude that Wrackspurts are fictitious. Nobody else has heard of them and they can be confused for a simple dazed expression. The fact that they are supposed to be invisible doesn't add to their credibility.
Things we can't be sure of, or about which there is insufficient information.
Moon Frogs
There is only one mention of moon frogs in the books, in The Quibbler:
...an interview with a wizard who claimed to have flown to the moon on a Cleandweep Six and brought back a bag of moon frogs to prove it...
(Order of the Phoenix, Chapter 10, Luna Lovegood).
Perhaps the claim of reaching the moon on a broom isn't as ludicrous as it sounds but it is still pretty unlikely. We have no source of frogs living on the moon outside of The Quibbler so have no real way of verifying the claim. We know that Harry finds the claim unlikely but that doesn't really confirm whether they existed or not (Harry is ignorant about an awful lot). We also don't know whether the wizarding community believed in moon frogs or not. People might think that moon frogs are real but find the idea of flying to the moon ridiculous. I think this one is open to interpretation.
Umgubular Slashkilters
Again, the Umgubular Slashkiltor is only mentioned once, by Luna.
"Well, my dad is very supportive of any anti-Ministry action!" said Luna Lovegood proudly from just behind Harry; evidently she had been eavesdropping on his conversation while Justin Finch-Fletchley attempted to disentangle himself from the robes that had flown up over his head. "He's always saying he'd believe anything of Fudge; I mean, the number of goblins Fudge has had assassinated! And of course he uses the Department of Mysteries to develop terrible poisons, which he secretly feeds to anybody who disagrees with him. And then there's his Umgubular Slashkilter -"
"Don't ask," Harry muttered to Cho as she opened her mouth, looking puzzled. She giggled.
(Order of the Phoenix, Chapter 18, Dumbledore's Army).
The Lexicon thinks that the Slashkilter may be a creature, and I'm inclined to agree with them. However, it could also be an object or a weapon; it isn't altogether clear from the context.
From Cho's reaction we could easily surmise that the Slashkilter is not widely known about or believed in in the magical community. We don't really have enough information to make an informed call on the Slashkilter.
Gulping Plimpies
Luna mentions these when describing the Gurdyroot in the quote above.
"Oh, it's a Gurdyroot," she said, stuffing the cat litter and the toadstool back in her bag. "You can keep it if you like, I've got a few of them. They're really excellent for warding off Gulping Plimpies."
(Half-Blood Prince, Chapter 20, Lord Voldemort's Request).
Now we know that Plimpies exist, based on the Fantastic Beasts entry cited above. However, it does specifically say there that Plimpies are an underwater creature. Luna seems to be carrying around the Gurdyroot when walking around overground in order to protect herself from these Gulping Plimpies. This makes me strongly suspect that they are a fictitious animal and that Luna is acting on superstition, not evidence. On this basis, it's likely that nobody else took the Gulping Plimpy seriously. They are only mentioned once, and very briefly, so I'm not sure we can be definitive.
Aquavirius Maggots
Again, these are only mentioned once.
The place was quite empty, except for a few desks and, in the very middle of the room, an enormous glass tank of deep green liquid, big enough for all of them to swim in; a number of pearly-white objects were drifting around lazily in it.
"What're those things?" whispered Ron.
"Dunno," said Harry.
"Are they fish?" breathed Ginny.
"Aquavirius Maggots!" said Luna excitedly. "Dad said the Ministry were breeding -"
"No," said Hermione. She sounded odd. She moved forward to look through the side of the tank. "They're brains."
(Order of the Phoenix, Chapter 34, The Department of Mysteries).
The maggots are a good candidate for a fictitious creature. Nobody else mentions them and Luna doesn't even seem to be able to identify them. The items in the tank are confirmed to be brains, after all, so the fact that Luna jumps to conclusions so rapidly is probably suggestive. They also fit well into Xenophilius's world of government conspiracy theories. Still, we have no firm statement saying they're fictional.
Nargles
These are only mentioned in one chapter, by Luna again.
"Mistletoe," said Luna dreamily, pointing at a large clump of white berries placed almost over Harry's head. He jumped out from under it. "Good thinking," said Luna very seriously. "It's often infected with Nargles."
Harry was saved the necessity of asking what Nargles were by the arrival of Angelina, Katie and Alicia.
(Order of the Phoenix, Chapter 21, The Eye of the Snake).
It's clear that Harry has never heard of Nargles and doesn't believe in them. Cho seemed to be similarly confused.
"Mistletoe," said Cho quietly, pointing at the ceiling over his head.
"Yeah," said Harry. His mouth was very dry. "It's probably full of Nargles, though."
"What are Nargles?"
"No idea," said Harry. She had moved closer. His brain seemed to have been Stunned. "You'd have to ask Loony. Luna, I mean."
Cho made a funny noise halfway between a sob and a laugh.
(Order of the Phoenix, Chapter 21, The Eye of the Snake).
Clearly she's never heard of them either. I think this is another case where the creature probably isn't real but it isn't possible to completely rule it out.
All in all, there are eight things which the Lovegoods believe in which are real and which are widely accepted (even if in two cases we can't be definitive that anybody else does), four things which they believe in which don't exist and five things about which we can't be sure. It's a mixed bag but it does at least show that not everything Xenophilius Lovegood believed in was absurd.
