I'd say that analysis is on point. Usually, when patrilineal inheritance and patriachical power dynamics aren't part of the ideological structure, the need to repress lgbt dynamics within the sexes and genders is less of an imperative. Although I would be cautious to simply equate third genders in general to nonbinary/trans identities of today, they always had their own, specific historical and ideological circumstances.

One example of what basically amounted to a "third gender" that was present also in western societies historically (although more so in other parts of the world), would be eunuchs. Created culturally (and very much materially by castration, of course) out of patriarchical concerns of inheritance and power dynamics, as a subset of people that won't endanger inheritance and without the risk of them creating their own dynasty, they were seen as having completely different roles as to their sexuation and overall status. (Of course, it is interesting to note, that the power dynamics shifted and their position as reliable advisors "without ambition" actually led to eunuch shadow governments, for example in parts of Chinese history). Of note is, that for example castrated choir boys (done so to preserve their "angelic" voices) in western society were one of the few examples where we have evidence of them being idolised as desireable by a female POV sexually (most likely because there was no risk of pregnancy and thus a much reduced risk of an extramarital affair resulting in being shamed and/or even killed).

So existence of a third gender does not necessarily entail respect for inherent identities of people. There are also some instances of third-gender identities being crafted basically to satisfy the sexual needs of dominant homosexual men in positions of power, often arising out of/develooing alongside male prostitution, within history.

I am a Marxist when looking at history, so I view patriarchy as something that arose out of material conditions as a very "succesful" model to reproduce class society in the past, which is why it became so prevalent globally, even without taking colonial history into account. Reducing women to their reproductive role, while also giving them a "valued as an object" status, was beneficial to societies that impose their will violently through war and repression. You can survive and rebound from losing two-thirds of your men in war as a society, but not losing your women. And in times, where warfare and violence was much more heavily tied to physical fitness, the statistical biological differences in human sexual dimporphism further positioned patriarchical structures as a tragically succesful model - which of course did not just do good things for men at all, their lack of being valued in an objectified way also meant they were more disposable, if not in a position of power.

More and more archeological evidence, combined with anthropological studies of non-class tribal societies, shows that on average, our ancestors in pre-history were much more egalitarian, as this was conducive, even necessary, to their survival (imagine a tribal society that had hard rules against women hunting, even if they are very much capable to do so, in a season/area where hunting is the main source of food at the moment. It would have been just stupidity. Same for men foraging, etc).

There is also evidence, that organised warfare as we know it today only started alongside the creation of class society, as soon as a surplus of food and overall resources allowed for a surplus of people - where taking the risk of losing 2/3rds of your men to conquer territory, slaves and the surplus of others suddenly became a viable strategy. (Although, it is important to note, that there is evidence of sporadic, often genocidal conflict in pre-history as well, but it is reasonable at this point to assume those were exceptional cases, and more often than not, conflict was avoided if at all possible. For a deeper exploration of the cultural differences that arose from that avoidance of war-like conflict, I'd recommend checking out Raymond C. Kelly's "Warless Societies and the Origin of War")

The material conditions of post-industrialised society open up the possibility again, of overcoming class society and with it, patriarchical society. Including finding a new dynamic for lgbt sexuation, sexuality and identity. That's one of the main reasons I view myself as a Marxist communist, pleading to re-invent and re-organise the communist movement without following Marxism-Leninism like a religious doctrine. IMO, the world will face crises in the coming decades that, on average, people today do not have the analytical tools and contexts to understand, many fleeing into either "maintain the status quo, we can do this somehow" or "everything will be destroyed anyway (so leave me alone and maintain the status quo)" narratives for the future. I say: learn how to organise, how to fight if you are able, connect with people, and be ready to take advantage of the coming chaos. There's no shame to be a bit of a prepper, but please without the individualism and conspiracy-mindedness of what the stereotype would be.

OK, sorry, I went on a bit of a rant there, hope it was structured enough not to completely overwhelm. History, philosophy and politics are my special interest, I can get easily triggered into just typing out a wall of text.