In Judaism, there seem to be several prohibitions regarding transgenderism:
The removal of genital organs is forbidden on the basis of the prohibition against "anything which is mauled, crushed, torn or cut" (Leviticus 22:24). A further prohibition in Deuteronomy 22:5 proscribes not only cross-dressing but any action uniquely identified with the opposite sex, and this would also apply to an operation to transform sexual characteristics.
Now, one of the Noahide commandment categories forbids engagement in sexual immorality. Does trying to change one's sex fall under this or would it be permissible for a Noahide to become transgender? Would things like this also apply to Noahidism?
Also, "by changing one's sex", I mean undergoing things such as hormone replacement therapy, genital surgical removal in cases of male-to-female transgender people (more generally, gender reassignment surgery), and potentially in the future, even things like uterus transplants.