That's not a particularly novel viewpoint. Pervert-in-chief Michel Foucault raised the argument that "homosexual" as an
identity didn't really exist prior to the 19th century. The mid 19th century saw the start of the argument that the "Urning" existed as a form of "spiritual hermaphrodite"; someone who had the opposite sex's soul (compared to a "physical hermphrodite") and then it became a system of classification, first as a psychosexual disorder before an actual social identity, with terms like "invert" or "homosexual" being coined in the 1890s.
Prior to that the discourse tended to be around homosexual acts as just something extra perverted that already perverted people do (think like Marquis de Sade) rather than a thing people were - so a man who had sex with men wasn't "gay", he was just doing a more shocking variety of sodomy. It's arguably not universal as Western culture pre 19th century does seem to have subgroups of people who understood themselves as having a particular shared identity, and likewise a lot of slang at the time seems to view them as a category of person, but Foucault's arguments were foundational to queer theory.
The irony would be in suggesting that therefore all these people fall into the category of trans. Western society did not tend to have third gender roles and treated crossdressing as something associated with homosexual acts, but also in general just a transgression by itself. Women tend to get overlooked because in the anglosphere lesbianism wasn't criminalised, but there's various cases from the continent of women being punished for crossdressing, including executed for pretending to be men with a strapon. Even in non-Western third gender societies, the third genders were typically viewed at best as something separate from men and women, if not a subcategory of that gender that had gone wrong, and the gender roles were highly restrictive.
The only societies that didn't accept homosexuality but sort of accepted trans people as being their gender are basically modern day Iran (due to a fatwa -
they're not accepted by many Iranians) and arguably 50s-60s Western society, where people didn't really understand what trans people were but had doctors claiming they could change sex through cutting edge science (and also were bad at clocking). This was mostly through them lying about being intersex,
which let them change birth certificates. As the concept of what a trans person was became clearer, that very rapidly changed e.g.
Corbett vs Corbett 1970 established that trans women were men and therefore could not legally marry a man.
In the described scenario where cultures fall back to a pre-industrial baseline with no urbanism, gay and lesbian people would probably end up being confirmed bachelors or spinsters respectively or otherwise pretending to be straight. That scenario would also mean no access to hormones or surgery. I can guarantee that people would not start recognising transgender people as "really" their gender in that scenario, although trans women may find a sideline being the village bicycle if there's a lack of women. Trans men would almost certainly not be treated as men, because they wouldn't be as strong as men... and also in those sorts of survival scenarios women are expected to have multiple children and raise them, so can't opt out of doing it even if their pronouns are he/him.