See, now it's not just the Yuan-ti being intergalactic dickwads, there was a legitimate military campaign that they fought in alongside other groups. They don't look like titanic assholes, and the only ones more afraid of their military than their enemies are the ones who fought alongside them as their allies and saw how effective they were. All the reputation, none of the logic loopholes, and none of the amoral genocide! Everyone wins!

Except for the warmongers who used to be in power on the other side. I imagine they lost pretty hard.

This could work well though, it would provide the large military conflict that I need for my own character's background.