Does he? I have never really thought about this, but a section in this answer got me thinking:
I am confident that students of other faiths would not be obliged to take part in or even attend the celebrations, at least not while Dumbledore was in charge. (The Death Eaters, on the other hand...)
From an archived interview with JK Rowling:
Has Voldemort or Tom Riddle ever cared for or loved anyone?
Now, that’s a cracking question to end with — very good. No, never. [Laughter.] If he had, he couldn’t possibly be what he is. You will find out a lot more about that.
Can you really imagine Voldemort following a religion (following being the operative word here)? Can you imagine him, for instance, prostrating himself before "Jesus Christ Our Lord"? Or even accepting the existence of a being greater and more powerful than himself? No, Voldemort loved and worshipped only himself.
In fact, he set up his own religion, for goodness sake! The Death Eaters functioned as a sort of cult, with their own beliefs, their own rituals, their own symbols, and of course their own god - one Lord Voldemort. How could he be a follower of another religion at the same time as being head of his own?
And of course, even if he had claimed to follow another religion, we know he wouldn't really have followed its maxims. I'm fairly sure that all real or at least fairly mainstream religions disallow acts such as murder and torture which Voldemort took such pleasure in. Even if he was, for instance, a Christian, he couldn't have been an observant one. Whether breaking all the sacred rules of a religion disallows one from being considered a member of that religion is something we could debate, but I'll just leave it at that: a point to be considered.
Voldemort would not want to claim any religion as his, even in name only, since he did not want to be ordinary. He wanted to remain separate and superior, so he would not want to be one of many members of a religion without any way of distinguishing himself.
“Firstly, I hope you noticed Riddle’s reaction when I mentioned that another shared his first name, “Tom”?’
Harry nodded.
‘There he showed his contempt for anything that tied him to other people, anything that made him ordinary. Even then, he wished to be different, separate, notorious. He shed his name, as you know, within a few short years of that conversation and created the mask of “Lord Voldemort” behind which he has been hidden for so long.”
- Harry Potter and the Half-Blood Prince, Chapter 13 (The Secret Riddle)
Being a member of an established religion, nominally or otherwise, would mean that he would then share a religion with the rest of its followers, with no distinction between him and the rest.
