I can't give you a page or a reference or link, but I can tell you this was told to me by Ronald D. Moore, under a professional situation.
When I was pitching to Star Trek: The Next Generation I had a couple stories that dealt with the effects on the Enterprise crew due to the religious beliefs of other beings. In one case, I had a story I pitched about an off-shoot of the Betazoid race I temporarily called the Gammazoids who were very religious and superstitious and considered Troi, for several reasons, an abomination.
Ron's response was that something to the effect that (and this is NOT an exact quote), "In Gene Roddenberry's universe, people will have outgrown religion and the problems it causes and live with the need for it." There was a little more to it than that, but that summarizes it. Now, remember, Ron went on to do Battlestar Galactica and has shown he sees the importance of religion as a motivating factor in human behavior. I think that shows he was not talking about his views as a writer, but was speaking specifically of the "rules" of the Trek universe.
Roddenberry did not have a kind view of religion and on that story pitch (and one other) Ron was clear to draw that line and say there was no religion -- not only for our characters, but for other species as well. Roddenberry wanted a universe devoid of religion.
However, in Star Trek (the original), we do see in Balance of Terror there is a ship's chapel, but we see it used for a wedding service and we don't see any hint of it being used for worship. We do see, in Bread and Circuses, a parallel Earth where Rome never fell and Christianity is just starting to spread in their equivalent of our 20th century, but none of the crew members on the Enterprise claim any affiliation with Christianity when religion is discussed.
But before anyone gets going on Sto-vo-kor or anything else like that, I'll point out that I was pitching before Gene Roddenberry died, and for reference, he died just about the time Unification, Part I aired. Note that after Roddenberry's death, we did learn about some Klingon beliefs (including Sto-vo-kor) and we also saw, in Deep Space Nine that the Bajoran religious beliefs played a major part of the storylines and, as pointed out in the other answer, Chakotay's Native American spiritual beliefs were referenced in Voyager.
So, while Gene Roddenberry didn't want religion as a part of, at least, Star Trek: The Next Generation, it was discussed in one episode of the original series and there was a ship's chapel (which we only saw used for a wedding). We also see that after Roddenberry died, while Earth religions were avoided, religion did start to enter into the storylines after Roddenberry's death.