How is it that Christmas and Easter are celebrated and observed at Hogwarts? The films depict both holidays but no Wiccan feast days are mentioned. Christianity has been intolerant of witches and wizards, the Vatican has been rather negative on Rowlings' Harry Potter series, but the movies seem to depict an armistice or acceptance of conflicting positions. Is the history of the Church's persecution just water under the bridge?
It's unclear whether you are asking why the author seems to approve of Christianity, or why wizards do in-universe, so I have attempted to answer both possible questions.
Given that the author herself identifies as a Christian the presence of Christian holidays is no surprise. I think her own words are the best answer to your question: "I don't take any responsibility for the lunatic fringes of my own religion." So she is dismissive of those groups which consider her books unchristian, but there is no reason for her to be negative about her own religion.
As far as why wizarding culture accepts Christianity, we can reasonably conclude that is is because many wizards in England are in fact Christians. There is no reason to believe otherwise. Just because a group is unpopular with more mainstream Christianity doesn't mean they can't identify as Christian. For example, many gay people in real life identify as Christian regardless of the fact that many branches of Christianity oppose homosexuality. The same phenomenon probably applies to wizardry.
Evidence of this is present in crystallized answer on another question :
That being said, in Harry Potter and the Deathy Hallows, Harry finds two tombstones with Bible (New Testament) quotes on them. His parents' reads "The last enemy that shall be destroyed is death" (1 Corinthians 15:26) while Kendra and Ariana Dumbledore's reads "Where your treasure is, there will your heart be also" (Matthew 6:21)
As ForceFlow mentioned, these holidays are largely based upon natural phenomena (celestial body positioning, crop harvests, ...). For example, most cultures have a celebration involving bright lights somewhere near the Winter Solstice. It goes by different names in different regions, usually a legacy name from the predominant religion (which often parked their celebration on top of an existing celebration of nature). Many cultures also have some sort of rebirth/fecundity holiday near the start of Spring.
When looked at in this light, there is nothing too surprising about any group celebrating on (or near) these dates and using some of local lingo and traditions.
It seems that the Harry Potter Universe and Muggles have different ideas on what a witch or wizard is.
Muggles think of someone in league with the devil or at least a pagan but that clearly is not the idea in the Harry Potter Stories. The ability to do magic is an hereditary trait and has nothing whatsoever to do with ones belief or even goodness or badness.
Therefore they could be of any belief whatsoever (especially Muggleborns). Jo has indicated this to be the case.