No, those shamans probably dressed as women all the time and were considered women because very few Indians had a conception of homosexuals. If you were a man attracted to men and liked it up the ass, you were considered a woman. That's in line with every other instance of crossdressing shamans and subgroups among Native Americans, and you can't even blame troon activism since there's a citation to a 17th century Spanish explorer noticing there were men dressed as women. Doesn't say what page, and I don't feel like fixing Wikipedia's mistake by actually going through that book and finding it, but I pulled up that book on Google Books and searched "sodomía" (sodomy) and got some results so it's probably true.
Most of the rest of that text is an interpretation by a single activist, the other parts by another activist. It probably reflects whatever Chile's "I'm 1/16 Indian" types believe their supposed ancestors believed, so either garbled nonsense read out of an old anthropology book or straight up invented shit.
There's actually something some Kiwi's here might not know since not a lot is written about it, but take with a grain of salt because, while it was said by natives, most of their info is passed down orally, so there is no way to verify what I said.
Basically, third genders were treated as one entire demographic. If you were gay, a "failed wo/man" (i.e. liked doing things not normal for your roll, like a woman choosing to join hunting or battle parties, or men preferring scavenging and dress making) or even just looked too masculine/feminine, you'd be assigned this "other". Same thing happened with people believed to be shift changers, or people who had such a close connection to an animal that they could turn into it. These people were either feared or scorned (shift changers were both, seen as traitors to their own race if they were a prey animal because they usually tried to lead the herds away, or a potential danger to the tribe if they had a predatory shift.)
These people often had entirely seperate huts outside the villages, and it wasn't unusual for them to have one of 2 things happen- be forced away from burial sites because they were too impure, or forced closer to these psudo graveyards because they were too close to the other world. (I.e. shift changers were allowed, troons and gays were not)
I don't think I was ever told the reason shift changers were forced there, but I do know the boomers very much still believe in it. I've heard several people of one tribe each go hushed if I brought up the potential shift changer by name, like it was a curse.
Despite what troons think, they have by far the most ridged familial structures you could make. You did NOT deviate for any reason, as it was seen as upsetting the natural order- the order they themselves find to be apart of and guardians for.
ironically it settled down a lot more with christianity, it's still looked down upon to be different, even being a bookworm or interested in studies are seen as too white and you will be outcasted over it.
source- my brothers MIL who is directly best friends with the chief, and my brother who most often helped village elders and got to hear a lot of deeply held beliefs they don't often share as reward.
Also to add- even if women were pretty butch, they were still usually not allowed to join parties, it was seen as too dangerous and women were too valuable, even the ugly ones. I can count on one hand from stories of various indigenous histories where a woman was even mentioned near a kill during a hunt, and were usually there to keep watch if they snuck with the warriors deep into enemy territory. I think 1 or 2 were solely about the woman being a true warrior, and it's because she did all the trials by herself with no help.
(I.e. kill an enemy with a dagger making no sound, ride out on a stollen rival tribes horses, count coux, or touch an enemy in their camp/steal their feather as proof and get back without being caught, and I think 3 or 4 other things specific to the tribe, but those couple are universal.
Edit: off topic but my favorite story regarding the last one, and the BEST story I've ever fucking heard, was of the last indian warrior. They were either apache or something else, not cherokee cuz those have been a joke tribe forever. Anyway, a very old warrior specific tribe, and he had to adjust the qualifications a little bit, but he did several WITH SOMEONE TO WATCH IN THE SAME. FUCKING. NIGHT.
He stole an enemies scimitar/sabre and stabbed them in the heart from behind, taking it and his scalp for proof of his first kill, (this earns 1 feather. Every feather on an indian is a life taken. It used to be done as young as 8 so it wasn't included in the rites, but he did because it was important to treat your first death with utmost respect. Dunno how the scalping part honored it but w/e) he managed to take some plans from a commanding officers tent while everyone was having dinner and never got caught, stole a fucking helicopter, and burned a bunch of their rations to cover the sight and sound of the theft of the copter (was near a forest)
Dude was crazy and fucking survived the front lines.
I think he unironically got an entire ass head dress from the amount of enemies he killed. I wish I could find the quote but I remember hearing him say something along the lines of "Today I avenged the historic fallen of my tribe with the deaths of German invaders and defended my home for more warriors to continue my path."