I think its funny that people have gone to the extreme of KoA for wearing the armor... I never said that would be the case... I just think that it was a bit odd that the Gith don't even mention it AT ALL. You are clearly wearing armor worn only by their clan/ people that has to at least raise a red flag.
An example:
(Spoiler ahead) Even Boba Fett and the Sheriff Cobb Vanth have to explain to Din Djarin why they are in possession of Mandolorian armor. They aren't killed for it, but it is of concern. Hell Mandos seem to have a slight issue with anyone but them owning Beskar
I myself have never been a DM, but here is why I think the Githyanki would AT LEAST mention the fact that a non-Gith is wearing the armor of one of their kin.
1) the description of Githyanki half plate is as follows: "This armour was forged to Vlaakith's standards under the exacting eye of a githyanki smith." this tells me that generally speaking ONLY Githyanki wear it. This debunking the creative idea of them getting it from Astral marketplace and is super common place for other races to wear it.
2) the Githyanki seem to be an arrogant, prideful, bigoted lot. They vew other races as lesser... so much so they are ignorant of them (Example: calling a tiefling a teethling).
3)Given that they have their armor made just for them to a specific standard tells me they care a great deal about their armor and take pride in its making and wearing it is a source of pride (much like their blades)
4) They already think you are garbage and now you DARE to sully their uniform? That might be like wearing purple heart without having earned it... not to mention IRL tend to question when you have something or do something they think is culturally theirs.
I will grant some of this is MY perspective that is being infused in to what I know of Githyanki (IE the guides don't really tell you out right)