I could certainly see people choosing to side with the NCR because they like their armor better, it certainly wouldn't be the first timwe people favored a specific faction in a game based on appearances. Myself, I'll decide based on whichever faction seems to fit my character more, after all, if I want NCR armor, I'm sure I can just loot it.
Caesar's legion will shoot at you if you wear NCR armor no matter what your rep is with them
If that's the case, you can just take it off when you're in areas held by them and only wear it when you're not going to be interacting with them.