Regarding the second paragraph, I agree with your estimate that most "spiritual but not religious" people might think this way. I was, at some point in the past, exactly there in belief-space - I identified as "spiritual but not religious" explicitly, and explicitly held beliefs along those lines (minus the "anthropomorphic" part, keeping only the "mental" or "thinking" part of the anthropomorphism for some reason).

When I later realized that there was no tangible difference and no existing experiment that could tell me whether it was true, I kind of stopped caring, and eventually the questions dissipated on their own, though I couldn't tell exactly why at the time. When I found LW and read the sequences, I figured out what had happened, which was fun, but the real crisis of faith (if you can call it that - I never was religious to begin with, only "spiritual") had happened long before then.

People I see who call themselves "spiritual but not religious" and also know some science seem to behave in very similar manners to how I did back then, so I think it makes sense to assume a significant amount of them believe something like this.