They however need to deny it because of their belief system.

If you accept that homosexuals are innate and unchangeable, you accept that sex is innate and unchangeable .

Yup, totally agree.

To add on to this: I wonder if TRAs have changed the definition of sexuality because that reminds them that their sex and sex-they-wish-to-be do not match.

E.g. take "homosexual transsexual" (HSTS). I believe the older generation of transsexuals do not mind this term so much, but I am sure TRAs would-- if you have a lesbian woman who transitions to identifying as a man, then calling her a HSTS is accurate but may dismay her because it reminds her that she is a woman attracted to women (if she were actually a man, as she aspires to be, people would call her straight).

Rather, TRAs have attempted to re-define what the words "gay" and "lesbian" and "bisexual" mean, and in order to avoid the sex-acknowledging word "homosexual", have deemed it offensive and avoided it.