So a little background on my current play through of the game I chose to kill LAE'ZEL rather than rescue her and I stole her armor for my Ranger to wear... when I run in to the Gith patrol... they say nothing about it... I would think they would have a HUGE problem with a wood elf wearing Gith armor...
Why do we think Gith care so much about their armor?
For all we know, there's an astral market where that generic armor gets traded left and right. It may be that the Gith are entirely used to seeing other people and races walking around in armor that looks like that.
They care about their silver swords; we know that. But their regular gear and such? I don't know. It's possible we're just projecting our own expectations onto them. Especially given the reality of what seems to be. We chalk it up to early access mistakes when it might just be that the Gith don't care.
