The simple molecule that makes you trip does nothing without the complex system of the brain to trigger - people can also trip out by sitting in a salt tank - it's the brain/mind that the religion and the trip comes out of, which is why they're similar. I agree that there's an esoteric core in most religions - but i think in general this is just more advanced mystical methods for consciousness expansion; a sub-set of this may be psychedelic use, but it's clear it's not required.
Your argument that it must be from psychedelics because how efficacious and practical they are for reaching certain states is a value judgement - an experienced mystic may see it as a false economy if the inexperienced seeker is in and out so fast and with so many distracting flights of fancy that not much of importance is absorbed; and what's more the seeker may get cocky about how much they know and end up not much better off. The experienced mystic may have learned that the long term disciplined ways allow fuller integration of these mental states (i'm not agreeing with the mystic necessarily, just saying he might think that); now you could say the same about experienced psychonauts handling their trips better, but then the distinction between fast psychedelics and long winded non-drug methods is less obvious.
There are traditions that explicitly don't have a drug-based core, and have no secret inner sanctum (eg buddhism) - it's quite clear where the revelation came from (buddha sitting on his bum in the jungle (maybe having a cheeky chillum i suppose)) and it's laid out how to try and replicate it, and drugs are not involved, esoterically or exoterically - just lots of yoga. If salt tanks can make you trip, and meditation and things like that are a form of sensory deprivation, then psychedelic plants are not required for the mind-trip that is religion - even if the resulting mind trips may dffer in intensity the content would be similar as it's based on the same source material.
Shamans exist all round the world - some of them have access to tasty psychedelic plants and use them; others have no easy access drugs, but they do the same type of magic, just using endurance, ritual, 'magic' and maybe tobacco to make them trip out. I'm perfectly willing to accept some, or even lots of religion have a vestigial esoteric core that may have involved drugs (especially ones that are closer to shamanic heritage), just not that all religions are secretly about drugs.