Exactly! It's a nonsense argument - in cultures that have additional 'genders' they're people who are pushed out of their own sex class, not into the other.
It is a very interesting cultural phenomenon, but in no way relevant to the TWAW argument (or at least not in support of it).
And a closer look at the details undermines the argument further. 'Additional genders' tend to occur in very sexist societies - as a solution to pracctical or social problems caused by the rigid sex divide, they usually apply only to 1 sex, and they have very different effects on the status of people in that category depending on their sex. Men in third gender categories are usually lower status than 'proper men'; women in third gender categories are on the whole permitted more social and legal freedoms than other women but arent necessarily of higher status - and are still always lower than men.
Afghanistan - bacha posh. Women were (and now are again) no allowed to do anything. Couldn't work. Couldn't leave the house unaccompanied. So a widowed or deserted mother with only daughters would starve. Solution - allow one of the girl children to be a pretend man to support the family, accompany the women when they need to leave the house etc. A strictly temporary arrangement arising from circumstances rather than identity. It lasts only until puberty, at which point she reverts to being a woman and will be be married off to a real man who takes over the role of provider.
Albania - women couldn't inherit property. Families with no sons died out and socially disruptive squabbling over inheritance ensued. Solution - in a family withoit sons a daughter could become a pseudo man (subject to various restrictions and an outcastsl status) to keep things going for 1 more generation in the hope that a nephew or great nephew could take over eventually. Burrnesha can own property and gain some of the privileges of men; but they aren't equal to men and they have to renounce the 'privileges' of women. Can't marry, can't have children, can't really socialise with anyone apart from other burrnesha.
Hawaai - the religion has godesses, no women are allowed in temples, so Māhū are allowed to represent the godess. Them not being women is the whole point.
India's Hijra - gay and effeminate men reviled and pushed out of society, outcasts in a system where caste really means something. Scraping a living as beggars and prostitutes.
Samoan faʻafafine are probably one of the nearest examples to the current western understanding of trans. They are widely accepted by society, not of lower staus (can inherit titles and become chiefs). They are men who take a female role in a deeply sex-divided society. But nobody thinks they're Actual Women. And making them into a separate category rather than simply letting men-as-men do 'women's things' again proves it's not an acceptance of any sort of gender fluidity or sex equality. They may be accepted, but they are still othered