While I understand the idea, since some ST species are higly spiritual, such a place would fail IMO. The DS9 temple is dedicated to the Prophet, and nothing else. But nothing else. There is (probably) thousand of beliefs in the galaxy. A single place for all of them would be useless, as some may require peace, others noises, some a lot of people, some being alone... For example the Vulcan like being alone to meditate, but it's not true for every species.
It would be like trying to make a temple for every cult on Earth, it's a good idea, but impossible to do.
Was just thinking what has become of earth religons in this time (well earlier in the week anyway)
My guess is it's flourishing, though likely not as widespread as it is today. Since Earth is a utopia where hunger is gone, need is extinct, and hate is purely personal where it exists at all, it stands to reason that no religion would see any reason to hate another, and thus there would be peaceful coexistence.
The continued rise of science would of course precipitate the rise of atheists, but humanity's newfound goals of personal realization and pursuit of one's loves rather than one's needs is equally conducive to a religious pursuit should one decide that it what makes one happy.
At any rate, to the OP: I don't think it would really be worth the time to make a chapel in STO. The religious centers in-game now are related to canon flavor and have been seen before, or their respective religions fairly well expounded upon so as to make including them sensible. We get neither of those things from Earth religion, and not enough from other species' belief systems to make a "religion-neutral" building worthwhile. If it were added, it would be a strictly RP thing - moreso than the Academies, one of which at least has some canon precedent.
Honestly it'd be a waste of environment dev time that could be spent on, say, a new ship interior, or a new ground zone with some content attached, or things like that.