Star Trek is pretty agnostic, or in some cases atheistic. The only person who is a strong believer is Worf and Klingons. There is no character in TNG through Voyager that you could point at and say he's such and such fait, except may be Chakotey, but it's unclear what his religion is.
Well, you have Kira, who was extremely religious, and Sisko did become more involved in the religious aspect of his role as Emissary.
I don't see how having some religious characters be some horrible thing to Star Trek. It didn't destroy Babylon 5. They don't need to beat you over the head with a Bible but it certainly would be a beneficial change to highlight the diversity of humanity.