Perhaps most notable are the Bugis oroané, makkunrai, calabai, calalai and bissu.

I don't believe any of those are what we are talking about here, Transgender people are not considered another gender in our society, we are explicitly talking about people who are neither man nor woman and identify as a such. Other cultures have other genders besides the 2 plus 2 more for transgender, but as listed in the same wiki you linked, they don't necisarily reflect what people actually are, and are merely ideas, abstractions, rather than true identifications, or refer to people who have both genitalia.

In your last couple of paragraphs, you seem to be saying, "it's not fair that nonbinary people don't have stereotypes/gender roles to conform to/face pressure to conform to"

No, what I'm saying is that it isn't fair for some one to have the ability to claim persecution based on an un verfiable claim of non binary status, where they can then also absolve themselves of societal responsibilities applied to gender with out doing anything. No other group can do that. It would be like if a group of people formed who claimed to be all races, yet no race in particular, they didn't prescribe to the race binary (you are either a race or not), not that they didn't believe in race as a concept. They then said said because they have no race in particular it is impossible for them to be racist, but because they are also all races they are offended by all racism, and then proceed to reap the benefits of racism and privilege found by other races. You didn't solve racism, you didn't do anything to both claim persecution at the mere mention of race, and utilize racism and privilege to your advantage.

The thing is, in the race example you can't claim your race. Other people define your race for you, so you can't just decide one day you are absolved of the hardships or historical context of racism. We all bare a responsibility to end these hardships, but if it were possible to have such a system we would merely be promoting further exploitation of the system. The people who took advantage of this would not be insensitivised to help change the system for the better.