It is my experience that there are a huge number of theists who would indeed consider so-called 'near-death experiences' (NDEs) as evidence – if not proof – of a soul and/or an afterlife. The truth is they are not and cannot in any valid and sound sense be considered evidence of an afterlife; they simply can't, it is a complete non sequitur. To substantiate this claim, I'll explain what WOULD be necessary in order to count as empirical evidence for an afterlife, and why such a thing is impossible to attain.
In a naturalistic worldview, our consciousness is a product of our brain; it is an emergent phenomenon of the network of neurons and the electrochemical interactions between those neurons that exists within our brain, and as far as science has been able to tell, this is indeed the case. So then, with that in mind, what would it take to demonstrate that it is possible for our consciousness to survive our death? Anyone with any sense, whether they are a theist or an atheist, should be able to see where I am going with this. In order for us to have valid evidence of an afterlife, it would have to be demonstrated that it is possible for us to remain aware and conscious after the complete and total death and destruction of our brain and the cessation of 100% of neural activity; in other words, complete and total brain death. We would have to completely rule out any possibility that our brain retained any activity whatsoever that could have resulted in these hallucinations.
Now, anyone who knows anything about neuroscience will know that this is completely impossible to test by definition, as such a thing would necessarily be fatal to the person it happens to. Total brain death is irreversible, there is no coming back from it; it is literally the death and necrosis of your brain tissue, specifically your cerebral neurons. And medical death does NOT equal brain death. Anyone who was supposedly brain dead and was subsequently revived (i.e. long-term coma victims, etc.) was clearly NOT actually brain dead, otherwise they wouldn't have been able to come back so we could ask them if they experienced an afterlife. Case in point, they are called NEAR-death experiences for a reason, namely that the person (and by extension their brain) is not actually dead while they experience them. Therefore, we cannot say that they are not simply the product of our brains, because there is zero evidence of any kind that consciousness is able to survive the destruction of the brain that science says produces it, and there is plenty of evidence that NDEs are just that: the result of brains that are under tremendous stress.
Now if anyone could think of some way that it WOULD be possible to test this, I would be very interested in hearing it, because as far as I can tell such a thing is completely - almost tautologically - impossible to test, as it would necessarily be fatal to the person. And there is my rebuttal to near-death experiences being valid evidence for an afterlife or a soul: they simply are not.