A little bit late(r) to the party, but in addition to vsz's excellent answer regarding the rational nature of the world (both the Real World and the Wizarding World), and the laws that govern both, there are also several pieces of evidence from within the books & movies that indicate that the WW is most likely as religious as the Muggle World. If not more so.
In the books & movies, we see some practices that demonstrate at the very least a veneer of religious sentiment within the Wizarding World, if not an outright practice of religion. While many commentators have derided JKR's work as being little more than cleverly disguised Satanism, I find it interesting that what little evidence we see in the WW --- as always, through the eyes of 11 through 17 year old children --- indicates that the thin whitewash of religion is actually Christian, not Pagan, and certainly not the mix-n-match of modern neopaganism.
- One of the first things we see in the movies is the Christmas celebration at Hogwarts. We've got a proper Christmas tree and Christmas carols, kids greet each other with "happy Christmas".
- We also learn about St. Mungo's Hospital. In the WW, St. Mungo lived in the 16th century, but the name also applies to a much earlier saint.
- We learn that Sirius Black is Harry's godfather. The role of godparents is of Christian origin, which would have been introduced into England at a very early time.
- Lastly, we find several interesting names engraved on grave stones in the cemetery in Godric's Hollow, at the church of St. Jerome. Harry's parents are buried at St. Jerome's. Their headstone is engraved "The last enemy that shall be destroyed is death", a passage from Corinthians. Since the Potters lived there, we can only presume that Harry was also baptised at St. Jeromes.
We also have Dumbledore's frequent disquisitions on what are essentialy Christian virtues, in specific, that of love. Not romantic love, but agapé love: the kind of love that most 16 year old boys don't have, the kind that sends them to sacrifice themselves bodily for their friends, schoolmates, teachers, and even the Muggles beyond the confines of the WW. Self-sacrifical love: this, in context, is a very Christian theme, making Harry almost into a type (theologically speaking) of Christ.
The Wizarding World is not a Pagan world, and certainly not a neopagan one! The Dumbledores and the Potters may not be openly & obviously Christian, but, more than anything, they are ethnically English, and that, historically, means Christian and specifically Church of England.
There's no doubt that in modern England, religious observance is low. Probably something like 10 to 12% of Muggles attend church regularly. With the 1692 Statute of Wizarding Secrecy, I'd actually expect witches, largely unaware of what's going on in the greater Muggle World, to be rather móre religious than their muggle counterparts as they seem to cling to tradition far more strongly than do Muggles.