Why people believe what they experience while tripping is one of the great open questions regarding psychedelics.
It is quite common for psychedelic experiences to feel "more real than real", and often what has been revealed under their influence can feel like The Truth with a big fat capital T.
I suspect that most people who become true believers after such experiences (and there are a lot of them) are just not very critical thinkers, and don't have a habit of questioning themselves, the world, or what they experience, and so are more liable to swallow the revelations they get line, hook, and sinker without critically diving in to them or coming up with alternate explanations for what might have happened.
Then there are the die-hard atheists and materialists/physicalists, who may be err on the other extreme and hand wave everything they experience as "neurochemical noise" or whatnot. There are a bunch of these also, and when I read their dismissive reports I often wonder how strong their experiences were and how many of them they've had.
Sam Harris, a prominent figure in the so-called "new atheist" movement, actually gave a strong dose of a psychedelic mushroom a try, and reported on his experience.[1]
It's a fascinating account, given by a clearly intelligent and famously critical, anti-religious physicalist which I personally expected to be very negative and glibly dismissive, but to his great credit he treated it very respectfully, seriously, and not dismissively at all.
He did not become a true believer after his trip, but it really made me suspect that if he'd continued taking strong doses of psychedelics even he would have.
Such powerful, convincing experiences are how religious movements start, and no small number of them have started from psychedelics. In fact, some have theorized that many (all?) of the world's great religions ultimately had their roots in psychedelic experiences (see, for example, Allegro's "The Sacred Mushroom and the Cross"[2]).
I hope one day there'll be some serious research in to what is going on here, beyond simply reporting that mystical experiences are common on psychedelics.
[1] - https://www.youtube.com/watch?v=yKGddvmU0fA
[2] - https://en.wikipedia.org/wiki/The_Sacred_Mushroom_and_the_Cr...