This is all speculation based on things I've heard, so take it with a big grain of salt.
I used to be on a forum with somebody who posted about having an excellent relationship with his dead wife. He said they interact regularly. He was not religious. Normally I would think he's a crackpot or somebody trying to sell something, but he was not either of those things. He came across as very honest and intelligent and sincere. The forum had nothing to do with life after death, but it came up occasionally. His other comments were always very rational.
There are others, e.g. Bernardo Kastrup, who think that there is a single consciousness, and that life as a human (if I understand correctly, any physical life) is like when somebody has multiple personalities. When we die (according to Kastrup) we "remember" that we are part of that consciousness.
I think panpsychism in general is a non-religious basis for at least the possibility that consciousness doesn't have to be physical. Consciousness could be fundamental.
To be clear, I don't believe any of those things, but I don't rule them out either.
The same goes for religious belief. My reasons for not believing might be due to perspective. I doubt that my dogs had any clue as to why I put them on a leash. I (and humans in general) could be in a similar situation, and that would change a lot. I suspect we are in a similar situation as far as making assumptions that work for us, but are not necessarily grounded in reality. I think it's very likely that there are things that we don't and maybe can't understand.