I’ve found myself musing (and even googling) over the past few days about these groups. I couldn’t find much, but there didn’t seem to be any indication that any of them were considered to be women within their societies. I don’t know how much access to single sex spaces exists in those countries where these “third gender” groups exist but I wondered how the claim that such groups have always existed interacts with the current western demand that these men are women and must be treated as such.
I think most of these groups were historically homosexual. The gender aspect was a way of socially signalling homosexuality. The complexities of these different kinds of cultural forms completely escape the trans lobby though - they all get appropriated as evidence that all these people were in fact "trans" avant la lettre -- which is cultural imperialism at its finest, despite the fact they also all complain about "western colonialism"!
Just because lesbian women in history cross-dressed, for example, this did not mean they understood themselves to be "trans" in the modern sense. Often clothes were one of the few ways of signalling gay or lesbian sexuality to others. And even women who believed themselves to have a "masculine" temperament did not necessarily believe themselves (or want to be) actual men. Dressing and taking on "masculine" gestures was often done for effect as a performance of alternative sexuality, or sexual desire, not as an expression of an inner "identity".
Even people who believed in the Havelock Ellis/Krafft-Ebing "inversion" theory of homosexuality did not understand it in quite the same way trans activists think of "trans" now (and most actually disliked those theories - the protagonist of Radclyffe Hall's The Well of Loneliness is actually profoundly disturbed by encountering them, and Hall was deeply ambivalent about them despite cross-dressing herself).
Doing something because it's the only way your culture allows you to express homosexuality, for example, or get an education, or live as an intersex person, or make your living as part of a marginalised community, does not mean that's the same as having an inner "identity". Gender ideology deliberately collapses the two.
It just doesn't seem to occur to many contemporary trans activists that dressing a certain way in order to perform a social signal (ie. to let other women know you are lesbian), is not, and has never been, exactly the same as "expressing an identity".
The very idea of "identity" is itself a recent, modern Western construction, which doesn't really replicate the way people lived and thought of themselves in the past, or map on to the ways people experience their lives and selves in other cultures.
The irony of activists who are completely caught up in extremely historically specific formulations of Western identity politics, then claiming they are liberating us from Western colonial ideas! It's completely topsy-turvy! (And dreadfully Western and imperialist of them 
)