I noticed that remark too and thought it was quite odd. OTOH, Star Trek has always stayed away from controversial issues like the actual real world religious practices of flesh and blood contemporary people. If Gene Roddenbury was still alive and active in the production of "Enterprise", I don't believe he would have not gone there either.
A generic statement, like what you mentioned, "Yes, I have a faith, but it's very personal to me", would have been appropriate.
I agree. However, I was a bit surprised that the religion question was not the usual set-up for a response dismissing religion as a silly superstition, discredited since the 21st century. We'ver certainly seen that one beore.
Or Majel Roddenberry, either, who now controls the enterprise (so to speak).
Roddenberry wasn't shy about promoting good old-fashioned "Americanism"; one episode in the original series features a planet where people have somehow come into possession of a U.S. flag and a copy of the Constitution, courtesy of an errant space probe (like Voyager in Star Trek: The Movie, the one with Persis Khambatta). And in another episode, a whole world has gone Gangsterland, reproducing 20's Chicago right down to the Thompson choppers and Packard getaway cars.
He wasn't too averse to sex in the first series, either -- Kirk hit on that yeoman enough times to get bounced out of Starfleet for fraternization -- so that he can't be said to have sheltered behind "barber shop rules" or "bar rules" for avoiding controversial subjects. But you're right, the series seldom portrays any human being as devoutly religious in any religion whatever. I can't think of any characters in DS9 who would meet that description as "religious". Commander Sisko becomes "the Emissary", but he's sucked into someone else's religion, and into interacting with Bajoran religious leaders and divine presences (who are explained away as various sorts of benevolent or malign [the Pa Reis] disembodied space beings). None of the other major species depicted in the DS9 series exhibits any strong tendency toward religiosity, other than the (enslaved and conditioned) Vorta.
As for themes that suggest scratching itches, I was struck by the number of Voyager episodes that revolved around group consciousness(es)......mostly involving the Borg or ex-Borg. In DS9, it was the Prophets and Pa Reis. Anyone else notice that?