Do we have any evidence that Stan even uses magic? AFAIK, (and I’m probably wrong, as usual) Stan might as well be a Squib! This, of course, would make his little problem in Book 6 even more improbable.
Except that Hogwarts charges no money and admits any magical student. Students aren’t expected to “fully exploit their magical aptitude” prior to attendence. And we’ve seen them admit, on numerous occasions, students with no supportive families or financial wherewithal, including Muggle-borns whose families don’t even know magic exists.
Unless you can find a way to explain away the fact that students don’t have to pay and are admitted no matter how little magical talent they might end up possessing, this seems baseless. It’s quite clear that even the seemingly least-skilled magic users are admitted - Dumbledore himself has stated that it’s open to anyone who can do magic. In the case of Harvard, admission is contingent upon being able to pay an enormous amount of money (whether by being wealthy or by substantially impressing scholarship committees) and having excellent test scores and high school or undergraduate records. It is simply not the case that Hogwarts excludes students on that basis. If they do, it goes contrary to things that have been clearly explained in the book. There’s a good deal of evidence to suggest that, indeed, Hogwarts is pretty open to all. And there just isn’t any evidence to explain all that away.
Well, in HP, magic isn’t a religion, it’s an ability. So I don’t really see why you couldn’t have witches and wizards of any religion. I just assumed most of the the HP characters are either Church of England or no specific religion.