They are a ranked structured society as it seemed tho as the dragon knight was directing her as her superior by rank, not as a male to female. I dont think in her culture their is a distinction of male roles to female roles. They are all breed warriors (to what I figured) and its all about rank and prestige to their goddess. Different than in Drow culture where its about rank, prestige, and what sex you are born as. Toxic or tame masculinity or femininity by cultural standards for the gith I don't think exist by how they live. So if not racism than over zealous nationalism. Much like Helots to the Spartans, they were 2nd rate citizens. I figure the gith see all other races as 2nd rate races.
But back to the point, apart from laezel. I think most of the other races have a pretty standard "humanistic" standard of masculinity and femininity that Larian can bring to life(besides the drow and their matriarchies).
We define masculinity and femininity as they apply to humans - not other species. Humans and elves would be the same species - as half-elves aren't sterile - but Githyanki were born on another plane of existence and are unlikely to be mammals as they lay eggs - there is no reason to suspect you could have a human/Githyanki hybrid. But their society is very much based upon toxic masculinity - like the Spartans you mention - and if the stories about the Spartans are true and not simply made up by Athenians, then I wouldn't consider the ancient Spartans, not to be confused with their modern descendents who don't act like that, human either in terms of humanity rather than biology. These traits are excessive versions of those commonly caused by how testosterone affects most male human minds - if Githyanki hormones affect all members of their species in the same way it makes sense that none of them would object and they would soon develop it to a toxic nature. Someone like Lae'zel born human would likely consider themselves to be a trans man, but Githyanki biology being different, there is no reason to suspect that Lae'zel considers herself such.