With the changes I think mating like squid, shooting both egg and sperm into a common area makes more sense. What would make even more sense is asexual reproduction given the insanity of it all.
And 2 Spirit as a third gender just means gay indian. It isn't really a gender, just a select personality distribution in some gays who want to feel special. That's not anymore a gender than a military badge of supposed honor. I'm of the age where gay wasn't considered a gender.... you had men or women and some with a messed up physical biology like a hermaphrodite (be nice to them). Being gay didn't change your gender. It's a purely made up recent thing, and likely won't last more than a few generations until the concept loses steam. But I suppose science could generate different sexes. But seems pointless, unless there be a caste system of sexes doing a singular type of hereditary labor. I don't like that idea either.
Two spirit absolutely did not mean "gay", where are you getting this?
"Traditionally, Native American two-spirit people were male, female, and sometimes intersexed individuals who combined activities of both men and women with traits unique to their status as two-spirit people. In most tribes, they were considered neither men nor women; they occupied a distinct, alternative gender status.