You can only make your assertions about trans people existing in non-Western cutures via a thoroughly colonial appropriation & misrepresentation of social roles in other countries.
The Muxe, Kothey, Fa'afafine & Fa'afatama as just a few examples, do not pretend to have become the opposite sex, but because they are ordinary people from poor countries, (Lavishly-funded) Western trans activists have no compunction at all about talking over them, instrumentalising their social roles to artificially inflate the trans constituency & secure advantageous decisions from international NGOs & supra-national bodies.
It's the sine qua non of "erasing identities".
As to your final point, sex differences exist, sex is immutable so on what rational basis do people who "change gender" claim access to provisions made for the opposite sex?