My response: I see the main objection would be the current scientific paradigm of materialism or physicalism which assumes that only material phenomena are real. Mental states, which would be how past or inter-life experiences would tend to be viewed, are considered to be epiphenomena which have no inherent reality but are mere outgrowths of physical brain functioning.
I'm not sure this is a fair representation of the current scientific paradigm. Of course it depends on whom in the scientific community you listen to. I've been watching some of the online lectures by Roger Penrose recently (he just got a Nobel). He's proposing some very interesting and definitely non-physical speculations about the non-computable nature of consciousness. He's not mainstream on these topics, at least amongst physicists, but he is a major voice. And there are others too, in the rapidly-evolving field of consciousness studies. There has always been a philosophical stream in Physics that thinks creatively about the consequences of quantum mechanics, such as non-locality, quantum entanglement, etc. Henry Pierce Stapp, David Bohm, etc. And anyway, is electromagnetic radiation, for example, best thought of as a "material phenomenon"? Perhaps the science paradigm is not best thought about as material vs. nonmaterial, but as falsifiable vs. metaphysical.