Does anyone know why Ulysses keeps acting like I'm a member of NCR even though I'm not? And also, why does the Courier's Duster at the end have the NCR design on the back? Seriously, I'm not NCR and I wished the game would recognize that.

Goes by your highest rep, so if you do not want the NCR version, you need to lower your rep with the NCR.

That's kinda stupid. They could easily have handled that better. Any ideas on how to lower my rep to just neutral with them?

do things to harm the faction you want to lower, or wear faction armor.