It seems what you’re describing here is what we have in the USA, except we call them gay men and lesbian women. Perhaps other cultures, call what we call "sexual orientation" they call a different gender. What others might you have? Cross dressers; men who like to wear women's clothes? Or drag queens; men who like to perform as women?Hijra, (India), māhū (Hawaii), vakasalewalewa (Fiji), fakaleitī (Tonga)...all refer to people with male sexual characteristics and assigned male at birth but who do not (and do not wish to) conform to male gender identity...most, if not all, of these go back centuries...in Fiji, for example, the idea of vakasalewalewa (meaning 'behaving as a woman') long predates the imposition of strict binary gender identity that came with Christian missionaries in the 19th century...as far as I can tell, many, if not most cultures have specific words for 'third gender' people that go back at least centuries...its only English that seems to struggle with a word (or several) for it...
The Bugis people in Indonesia recognize 5 genders and apparently has done so for at least six centuries.
Is that enough or do want some more?