(1) There's a very interesting story in Harper's Magazine this month by Ian Buruma that makes more parallels between the outlook of the progressive left and Protestantism. I largely agree with your characterization of what is going on when "people say things like" the points you raised. I think it's more than likely that people are taking a religious-style attitude. The second half of your article provides the better evidence for this.

(2) However, I'm not sure the observations you make in the first half are particularly compelling in this regard. There are all manner of psychological conditions where the mental model someone has of their body has a mismatch with their body. From phantom limb syndrome through to an elderly man overestimating his athletic ability, this sort of thing is neither rare nor religious in nature (it's just biology!)--even if people say things like "I feel like a young man in an old man's body". Just as anthropomorphic language when used as a shortcut does not imply a belief in anamism ("the car doesn't like it when you turn the steering wheel too far to the right"), neither necessarily does deploying the language of soul or spirit imply that one is thinking religiously.