Picard was actually very articulate on the subject in Where Silence Has Lease. When Nagilum in the guise of Data asked Picard about his personal belief concerning death, Picard stated that he did think that the self survived the demise of the flesh. Picard believes our existence is beyond scientific understanding. TOS didn't seem to have any difficulty in this area, we saw some Human characters with overt sights of faith. Kirk with his "the one" statement made his position clear. The 24th century series do seem to have more of a problem with it's completely Human characters, and making clear where they stood on faith. Largely we don't know what they believe in, one way or the other. It was the half Human Deanna who seems to believe in fate (Pen Pals). On Voyager, when a story involved a character having a spiritual revelation (Barge of the Dead), it was the half Human Belanna and not one of her 100% Human shipmates. This is something I have a problem with. It's kind of like the planet with one people, one climate, one culture, one mode of dress. All of the the Federation, and all of Humanity, are not going to have the exact same position on faith, spirituality and organized religion. Some will be pro, some neutral, and some negative. Somewhere in the 150 plus mix of Member worlds of the Federation, there just might be a "planet Vatican."