Near death experiences and out-of-body experiences certainly happen, in the sense that people have these subjective experiences. NDEs are, however, still-alive experiences. And nothing actually leaves the body in an OBE. I'm a bit curious what Peterson can have said in his presentation, because I think that physics has in fact proven that nobody's mind or soul or spirit or whatever can really leave their body in any objective way. I wonder whether Peterson has any real grasp of the issues involved, or whether he just blithely rambles about how science doesn't know everything.
We can certainly have souls, just in the way that books have stories, not in the way they have binding glue. The notion that consciousness is something like a story written in the brain is the default scientific hypothesis now, I think. It's sometimes called the "strong AI" theory, because if mind is a matter of form, rather than of substance, then it should be perfectly possible for algorithms to be conscious. The neuroscience of consciousness is probably in an even more primitive state of infancy than artificial intelligence, currently. Both are likely to be active scientific fields for a long time, even if progress in them is slow. So it's not true that science has no interest in souls or can have nothing to say on them, if by "soul" one means ... everything anyone has ever wanted "soul" to mean, except for the otherwise irrelevant property of being substantial.
A soul that is a story-like pattern rather than a substance could have life after death in the way suggested in Ben Franklin's
unused epitaph. The story could be reprinted in a revised edition, or perhaps translated into another medium. We could be as graphic novels now, to be made into movies. Science is not likely to have anything to say about possibilities like that—for or against—since they would be happening in a whole other universe.
It seems to me that most traditional religious belief systems can easily abandon traditional conceptions of souls as substantial objects, and embrace strong-AI-like pattern theories of how souls relate to matter, without thereby losing anything significant from their traditional doctrines. It should be about as painless as accepting that the water in the ancient River Jordan was composed of H2O molecules. Believers may have thought of souls as substantial things for centuries, but insofar as substance dualism was ever really a part of most religions, it was always a loose part that could be pulled out without disrupting the rest of the structure.
The only exceptions I see would be religions that are for some reason committed to explicit doctrines about the material nature of spirit. I think these religions may be in about as much trouble as religions that explicitly denied the existence of atoms would be.
