But the one thing you're overlooking is your character also is a Githyanki, and would not tolerate such behavior from her. Her actions would come to blows starting with your first meeting, and many others along the way. Her attitude toward "lesser" races is one thing. But that attitude toward another Gith? I don't know, but don't think so.
Well, i admit that i do not have definitive answer for this matter ...
But speaking from my point of view, i see no reason why wouldnt you. O_o
I mean, if you talk with Lae'zel a lot, at some point she admits that she was litteraly killing other Githyani during her training, and express no remorse or regret.
That allone give me expression that Githyanki are not playing nice with each other, if you want someone respect ... you have to earn it yourself.
But i admit that once you are in the camp, and therefore you have spare time ... it would be really nice if you could challenge her to a duel, bcs "you have enough of her attitude", or bcs "you want her to admit you as a leader of this group" ... and then just beating her ass to obedience (wich in my opinion should give you +1 to her reputation).

Our created character is supposed to be "the main character" of that story arc.
That is completely irellevant if you ask me ...
It might be part of your story, that she was underestimating you at start, bug later on she recognize value of your methods.
In other words no, "main character" should never mean "the brithtest, strongest, fastest, and in all other ways the very bestest being in the universe, admired by everyone" ... that being have different name: "Mary Sue".

As a side note, it seemed a bit more difficult to raise her relationship level playing through as a Gith. It seemed much easier playing through as both a Lolth-sworn and Seldarine Drow.
I never tryed to romance her with anything but a Gith ...
And all i can say is that i never had any problem. o_O
Oh and one thing I also forgot, was her calling you "istik (or what ever that name she used is)
I didnt find the meaning of the word too ...
It seemed to me that its suppose to be some semi-pejorative word for "non-Githyanki", simmilar to Gaijin from Japaneese ...
But the Reddit seem quite certain that this word meaning is actualy something like "fool" ...
So yes, she is insulting you ... but not so hard so it would be totally unbearable.
So i admit, maybe it could cause some bad blood between you, but personaly i would presume that Gith are so pragmatical race, so they would first deal with the more pressing matter, wich is that they were infected and are on Ghaik ship in hells.

//Edit:
It would be appreciated tho, if Larian offered us some translation ... after all, IF our character is Githyanki, it should be perfectly aware of meaning of that word. :-/
Personaly i would imagine it as: Blahblahblah blah blahblahblah blahblah Istik(
:Fool) blahblahblah blah.
