While it was never stated in TOS there was no religion, I think it highly likely that, given the time travel technology available, by at least the TNG era religion would be greatly reduced, if not eliminated.
The reason I think so is that Federation scientists would have time traveled invisibly to see the formation of said religions to see if anything supernatural actually happened. And as an atheist myself, I find it very likely they will find that nothing supernatural happened at all.
These research results would be published, and religious attendance would definitely decline. Of course some would say the scientists are wrong etc (the Bajorans still think the wormhole aliens are gods), but many would believe them.
Voyager even traveled to the Big Bang in one episode, and there was nothing indicating a divine intelligence behind it at the time. Add into the fact that people like Q exist, and I think invisible Earth deities who never show up can't begin to compete with documented Q feats and appearances.