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I don't know much about the "last Christian alive," but the bit about the narrator on the moon and the gender swapping made easy remind me of the John Varley story "The Phantom of Kansas." It was originally published in 1976.
Here is a link
to a short description of it - might help you figure out if this is the story you're looking for?
Sorry, that's not the one. Thanks for trying.
This is a short story I read in Russian perhaps 15 years ago (I believe it was a translation. It might have been a novel, I'm not sure). It was printed in a newspaper in pieces, I only read two or three parts. The story is told by a male narrator who is on the Moon along with a woman. They meet what appears to be the last Christian alive (The narrator states he follows some weird faith the symbol of which is like a + sign with a long vertical bar). The ending has him and his companion together, but, IIRC, both have changed gender. Apparently, the narrator was born as a girl, but it was changed a few hours later.
Edited by Omeganian