So what?
What has that to do with the question of whether sex is an important characteristic in some circumstances?
It is possible that by studying other cultures, we might learn and grow and improve how we handle things.
Sure, that's possible. But let's also use some sense, and make sure that what we adopt from other cultures makes sense and is beneficial. Just because some other culture has a third gender role within their very strict sex-based hierarchy doesn't mean that it would make sense for our cultures to follow suit.
India has traditionally had very strict divisions on the basis of sex. There is work that only men can do, and work that only women do. Women have been treated as less-than-men for a very long time, and even with the progress they've made today women are treated as lesser and it's a fairly misogynistic culture. Yes, India has a hijra category - specifically for men who aren't man enough to be considered real men. It's largely been a category for gay men to be shoved into. It lets those men still be recognized as "better than women" in terms of social status, but "lesser than men". They've traditionally worn female-style clothing as an indication of their social status as hijra.
Now, that's great in the sense that not-very-manly-men aren't beaten up or abused. I support that. On the other hand... I don't think that's a great thing for the US or other english-speaking cultures to
adopt. I don't think that social status should be tied to sex - and I don't think you would like that either.
I think it would be far superior for our cultures to take a different approach altogether. I think we should focus on eradicating gender roles and expectations altogether. I don't think there's anything at all wrong with women wearing steel-toed boots and flannel shirts, there's nothing wrong with a woman being butch or mannish in presentation - it doesn't make her any less of a woman. The butchiest butch lesbian is still just as female as you and I are, and that's fairly well accepted.
Men face more scrutiny. On the whole, men are not as accepting of effeminate men than women are of butch women. We don't care if a woman wears manly clothes... but men in general seem to care quite a bit if a man wears womanly clothes. Men gatekeep masculinity far more strictly than women monitor femininity - and you can thank our feminist forebears for that.
To me, it makes way more sense to spend our efforts convincing men that a man in a frilly skirt is still just as much of a man as a man in dungarees. I'd far rather focus on shifting our culture in order to allow ANYONE to present however they want than on enforcing gendered expectations.