Clearly the term "mudblood" is a slur in the Harry Potter universe. Is there a polite way for witches and wizards to talk about magical people born of muggles?
Yes, at least three
Most prominent is, of course, Muggleborn (or "Muggle-born" when used as an adjective). Ron draws an explicit distinction between the two terms in Chamber of Secrets1:
"Mudblood's a really foul name for someone who is Muggle-born — you know, non-magic parents. There are some wizards — like Malfoy's family — who think they’re better than everyone else because they're what people call pure-blood."
Chamber of Secrets Chapter 7: Mudbloods and Murmurs"
And it's good enough for Dumbledore, which is good enough for me:
"And imagine," Dumbledore went on, "what might have happened then... The Weasleys are one of our most prominent pure-blood families. Imagine the effect on Arthur Weasley and his Muggle Protection Act, if his own daughter was discovered attacking and — killing Muggleborns... Very fortunate the diary was discovered, and Riddle's memories wiped from it. Who knows what the consequences might have been otherwise..."
Chamber of Secrets Chapter 18: Dobby's Reward"
North American wizards have their own version of "Muggleborn", No-Maj-born, which is used on Pottermore:
Pure-blood families, who were well-informed through wizarding newspapers about the activities of both Puritans and Scourers, rarely left for America. This meant a far higher percentage of No-Maj-born witches and wizards in the New World than elsewhere.
Pottermore History of Magic in North America: Seventeenth Century and Beyond
The Pottermore article on "pure-bloodedness" mentions the word Magbob, an archaic term from the time of the Hogwarts Founders, which evidently fell out of use in the intervening centuries (emphasis mine):
[Salazar] Slytherin's discrimination on the basis of parentage was considered an unusual and misguided view by the majority of wizards at the time. Contemporary literature suggests that Muggle-borns were not only accepted, but often considered to be particularly gifted. They went by the affectionate name of 'Magbobs' (there has been much debate about the origin of the term, but it seems most likely to be that in such a case, magic 'bobbed up' out of nowhere).
1 Hat-tip to Au101, in comments, for suggesting I include this quote
Witches and wizards of Muggle birth are referred to as "Muggle-born" or "Mudbloods". Harry told Horace S.
One of my best friends is Muggle-born" [HBP, Horace Slughorn]
Likewise Hermione describes herself with the term "Muggle-born".
I'm Muggle-born, you see. [HBP, The Half-blood Prince]
There are plenty of examples where "Mudblood" is the preferential insult Malfoy hurls at Hermione.
don't touch my hand, now. I've just washed it, you see; don't want a Mudblood sliming it up. [GoF, The Weighing of the Wands]
There is a confrontation between James P. and Severus S. where the latter calls her a Mudblood.
I don't need help from filthy little Mudbloods like her! [OotP, Snape's Worst Memory]
James wanted Snape to apologize and he told Lily he'd never call her that.
The polite way is the clear indication of their parentage, "Muggle-born", or Witch or Wizard.
Muggle-borns or Half-bloods as it may be.