It seems quite hypocritical that Thingol wouldn't let Beren marry his daughter yet he is married to a Maia. Thingol came upon Melian and instantly fell in love with her in Beleriand, then Beren comes along in the same fashion Thingol did and yet he isn't allowed to be married to her. Why is this?
This is answered explicitly in the text (emphasis mine):
Thingol looked in silence upon Lúthien; and he thought in his heart: 'Unhappy Men, children of little lords and brief kings, shall such as these lay hands on you, and yet live?'
The Silmarillion III Quenta Silmarillion Chapter 19: "Of Beren and Lúthien"
Thingol's objection is twofold:
Men are comparatively low-rank. This is classism as much as it is good old-fashioned racism; at this point in Middle-earth's history, there are no great kingdoms of Men. Although there are the Three Great Houses, they're just tenants of the Elf-lords, rather than lords in their own right. It's not until the Second Age that we get the first real Kingdom of Men.
They're mortal. This one is just racism, basically. But bear in mind that there's no precedent for an Immortal marrying a Mortal; although Thingol married a Maia, they're to fairly similar beings, at least spiritually. For Thingol, who at the time of this tale has lived for thousands of years, 30-year-old Beren seems rather unimpressive.
Although it's not touched on in this instance, there is a practical edge to this complaint, which Tolkien addresses in an essay titled "Athrabeth Finrod ah Andreth." The essay is the text of a discussion between Finrod Felagund and Andreth, a human wisewoman; the two talk about a number of things, but most relevant for our purposes is a discussion about he potential of a relationship between Andreth and Finrod's younger brother Aegnor:
'I would not have troubled him, when my short youth was spent. I would not have hobbled as a hag after his bright feet, when I could no longer run beside him!'
'Maybe not,' said Finrod. 'So you feel now. But do you think of him? He would not have run before thee. He would have stayed at thy side to uphold thee. Then pity thou wouldst have had in every hour, pity inescapable. He would not have thee so shamed.
'Andreth adaneth, the life and love of the Eldar dwells much in memory; and we (if not ye) would rather have a memory that is fair but unfinished than one that goes on to a grievous end. Now he will ever remember thee in the sun of morning, and that last evening by the water of Aeluin in which he saw thy face mirrored with a star caught in thy hair - ever, until the North-wind brings the night of his flame. Yea, and after that, sitting in the House of Mandos in the Halls of Awaiting until the end of Arda.
History of Middle-earth X Morgoth's Ring Part 4: "Athrabeth Finrod ah Andreth"
Finrod's argument is that, had they married, Aegnor would have remained faithful to Andreth for her entire life, as she aged and died and he remained perpetually young (which is consistent with Elvish tradition; they mate for life, and re-marriage is exceptionally rare). That would have been incredibly embarrassing for Andreth, who would have felt like a burden on her immortal husband, and would have saddened Aegnor to have to remember her as an invalid.
Although we can't be confident that Thingol was thinking about this at the time, it does lend a certain legitimacy to his point of view; it's just bad news for all concerned.
Because Beren was mere mortal
Yes, he married "above someone above his class", but if you look closely there is not that huge difference between Maiars and Elves - they can both be quite powerful, they are both favored by Valars - and most important, they are both immortal.
Now imagine this situation: you are a king and a father to the most beautiful girl, and here comes a bad boy without a penny to his name that wants to marry her. Also, he will abandon her in a blink of the eye (what is a mortal life span to immortals elves?). And since (most?) elves are highly monogamistic (mating for life and not looking for new partner when the current one dies) this would leave Luthien heartbroken and scarred for life. As a responsible father he had no choice but to deny/give impossible task to fulfill as a condition to the marriage.
Was it hypocritical? Maybe. But totally understandable.
This is a complex question because there are actually two main reasons why Thingol distrusted Beren. As has been noted, Beren was mortal and therefore Thingol knew that he would lose his daughter to a fate that he did not comprehend, i.e. death. Thingol knew that those who married would share the same fate. The second most important reason why Thingol mistrusted Beren and tried to get him killed (by sending him on a doomed errand to get the silmarils), is that soon after men first entered Beleriand he experienced terrible dreams about their coming, and he experienced these dreams before any information about the existence of men was actually available. From Melian's prophecy we can probably assume that the content of his dreams somehow involved the notion that the coming of men into middle earth would lead to the end of his kingdom and/or to his own demise. Thus the sudden emergence of a mortal before his throne was an ill omen that he needed to get rid of. Note also that this was not just paranoia on his part because his troubled dreams turned into reality.
It is said that in all these matters none save Finrod Felegund took counsel with King Thingol, and he was ill pleased, both for that reason, and because he was troubled by dreams concerning the coming of men ere ever the first tidings of them were heard. Therefore he commanded that men should take no lands to dwell in save in the north, and that the princes whom they served should be answerable for all that they did; and he said: 'Into Doriath shall no Man come while my realm lasts, not even those of the house of Beor who serve Finrod the beloved.' Melian said nothing to him at that time, but afterwards she said to Galadriel: 'Now the world runs on swiftly to great tidings. And one of Men, even of Beor's house, shall indeed come, and the Girdle of Melian shall not restrain him, for doom geater than my power shall send him; and the songs that shall spring from that coming shall endure when all Middlle-earth is changed.' - Silmarillion