Fascist propaganda is independent from facts and logic.

Surely that'd depend on the Muslim? Like, Islam is a very large religion and religious people rarely follow or consider valid all their stated rules to the letter, and disagree with eachother over the interpretation of those they do. I don't know what exactly the Koran says on the matter, but given the terminology and understanding around gender (and available technology for transition) has changed a fair bit since the time it was written, I'd be fairly surprised if it said anything as clear as "you must not be trans" that didn't leave room for interpretation and disagreement.