Looks like the lazy assumption that Islam is the problem here might not be accurate:
(from hrc. Org)
"As early as 1988, gender reassignment surgery was declared acceptable under Islamic law by scholars at Egypt’s Al-Azhar, the world’s oldest Islamic university. In Iran, in 1987, Ayatollah Khomeini declared transgender surgical operations allowable. The basis for this attitude of acceptance is the belief that a person is born transgender but chooses to be homosexual, making homosexuality a sin. Nevertheless, many transgender Muslims after reassignment surgery suffer rejection, socially and culturally, in their own communities due to their remaining in their place of origin. If one is unable to relocate to another region where they are not known, they often suffer verbal and physical violence."