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.
Kira is not Starfleet and Bajor not part of Federation. They had only discovered a short time ago that the prophets are actually aliens that live in a wormhole. Give them time to adjust, old generations to die, and young ones to grow up, you'd see the difference.
Sisko never believed in them as prophets but aliens.
Picard believes that there is something out there, and McCoy, who usually uses phrases like "My God" and is considered to be religous by some fans, flat out states that according to myth, Earth was created in 6 days.
No one is stating that you won't have a spiritual person here and there, but Star Trek has always been about rationalism, and there is no need to have characters go to a chaplain on a regular basis. That would indicate a widespread belief abord the ship which is rediculous because none of them believe from what we know. Why would they go to chaplain? So they can pray to whom?