I strongly believe they had religion.
Well, there is the Fat Friar. I’m pretty certain that a Friar is found only in Christianity, Catholicism to be precise. I don’t know if protestant forms have anything like the Catholic orders. Since Hogwarts goes back before the protestant revolution, it makes sense that he would be a Catholic Friar. Of course, he might not have been a pure blood. Also, Dumbledore, who is also not pure-blood, but well respected by most none the less, clearly at least read the Bible, which is of course, Christian. We can deduce this by the fact that it must have been him that put the verse from Matthew 6:21, For where your treasure is, there your heart is also, on his sister's tombstone. I guess Aberforth could have done it, but that would still show a wizard was familiar with The Bible and there is also speculation that Dumbledore is the one who had the verse straight from 1 Corinthians 15:26, The last enemy to be defeated is death. put on Lily and James' tombstone, in the church yard cemetery. Who else would have done so? Yep, Dumbledore read the Bible.I don't think that they would agree with a Muggle religion like Christianity, but this is a matter of opinion.
As others point out, there is also the fact of the celebration or at least acknowledgement of Christmas and Easter, which are Christian. Regardless of how many still actually practice, as in the real world, it is evident that they have a history of religious practices, so we can assume that some at least still do.
There is also the wizard dressed in black who conducts Dumbledore’s funeral, if I remember correctly. I automatically pictured a priest or minister of some sort. Who performed the Weasley wedding? I can’t remember that. I choose to believe they had clergymen of some sort.
I think it is highly likely that the religious members of the wizarding community in Britain would have been majority Christian, as Christianity was the predominate religion for centuries, but it is reasonable to believe that the Patil twins could be Hindu, and that there were other religious traditions represented, just as in the real Britain.
And yet they can’t explain many things like the Shroud of Turin, stigmata, medical miracles…. They can’t explain things like the origins of life sufficiently to rule out the need for a Creator, though they will say they have. Stephen Hawking, smart as he may be, can say it just happened spontaneously, all day long, but just because he says so does not satisfy the scientific method. His M-theory is just that, a theory. It supposes all sorts of things that can not be studied, witnessed, observed, verified… Yet he declares it as if it is confirmed and proves there is no need for God. Well, pfft…If you say so Stephen. The Big Bang needed something to start from; where did those first subatomic particles come from? Where did the energy originate? Where did the first seeds of that first primitive life form that slithered out of the primordial muck come from? Nothing comes from nothing, yet some scientists would argue that something came from nothing because what is nothing really isn’t nothing, so… *dizzy* Honestly, belief in some of their claims requires just as much or more faith as belief in God. I love science, but it hasn’t been able to explain everything we see and some people refuse to see what science shows if it supports things they don’t want to believe. The scientific study done on the Shroud and more specifically the sudarium (the facecloth of Jesus) is incredible.Muggles have science to explain what we see, so some people now say well that renders the idea of a god or gods a moot point.
I completely agree that it might be even more likely for the wizarding world to be religious. I think the ability that the wizards have to seemingly create stuff out of thin air would only convince them more of the need for a Creator, particularly when they can do so much, but still can not create permanent things like food and clothing, etc…( Gamp’s Law that was referenced above) And as stated, they can not create life; they can not stop death or raise the dead to life. They may have special power, but they are far from all powerful. Plus, they do have the veil, where they can hear the departed. Afterlife….
As a Christian, however, this issue gets more complicated. Many Christians believe Witchcraft to be wrong, so does this mean that the wizarding world can't practise Christianity? This is where I get confused.
I think the problem some have with the idea of 'religion' in the potterverse is the equating of the 'magic' in Harry Potter with the sort of 'magic' or 'witchcraft' that the Church does condemn. Harry Potter's 'magic' is not the type of magic we can go down to Barnes and Noble and get a book on to help us cast spells. It does not call upon 'spirits' 'earth spirits', etc... It is not a form of worship or practice like Wicca, paganism, etc. that one decides they are going to do in opposition to what the Christian faith teaches. I think it is very interesting that JKR, who describes herself as a Christian, made Divination a ‘very woolly subject’ and showed that the reading of tea leaves, ball gazing, etc. didn't really seem to work. McGonagall had no use for it and Dumbledore was even going to discontinue it. But for the need to keep Trelawney close by after the prophecy, he would have. Only when she was not trying was she ‘gifted’ with the sight of prophecy.
Anyway, the magic in Harry Potter is an (imaginary) ability that people are 'born with' similar to gifted musicians or artists. As Michelangelo had a gift from God to sculpt, Harry Potter could be said to have been gifted with magic. No matter how a non artistic person tries, they will not be able to do what Michelangelo did; likewise, no matter what a "Muggle' does, he can not perform the type of 'magic' Harry had. A wizard who was a believer would know that they were not calling on forces outside themselves or from other than God to perform it, and so they would know their ‘magic’ was not against God’s laws, but a gift fom Him. Therefore, in these fictional books, we have a fictional magical Fat Friar. I do think the persecution might have made them anti-Muggle, but not anti-God, or Jesus.
I think there was also mentioned a painting with some moving sinister looking monks. Monks are also religious. And of course, there is the biggest hint of all, the revelation of the afterlife, and damnation, as we see with the portion of Voldemort's soul, which is definitely a religious belief, even if not specific to a particular faith. The fact they have proof of the soul is pretty huge too, actually.
So yes, though JKR intentionally left religion very vague, she definitely dropped hints of it around, so I think it is within Canon to explore it. I would go so far as to say a story about Harry’s conversion after his experiences in DH would be quite appropriate. Who is going to come back from a near death experience, after meeting a ‘dead’ person, witnessing a withered soul, and not be changed? And why would it be necessary for Voldemort to repent?
Religion…it’s in there!
/My 2 cents…okay, maybe 20 cents.