I once read a short story in a magazine (most likely Asimov's or Fantasy and Science Fiction) about reincarnation.
Society has developed a way to identify past lives. I think it was a machine of some kind. It was and "in" fad to find out your past lives and tell people about them.
One of the rules was that a person could not claim to have been the reincarnation of certain souls. Jesus was one, Buddha was another. There may have been others. I think the claim was that no one could be the reincarnation of those people, but the authorities would come for you if you claimed that you were.
I think the story began with two guys sitting in a cafe, one telling the story to another... a journalist maybe?
The story was about a girl who was claiming that she was the reincarnation of Jesus. Over the course of the story, the narrator becomes convinced that she is telling the truth. Eventually "the State" catches up with her and she disappears.