It’s less state dependent than you think. The feds have the last say in the safety equipment that comes on your car from the factory. They write the regulations on safety equipment for all highway vehicles.
You're right that they regulate the safety equipment that is required to be on from factory, but the states nearly copy/paste those and make them statutes in their jurisdictions. I have never seen a federal traffic cop. It is the state's law enforcement arm (the various state troopers, county deputies, and all the forms of police) that enforces the traffic code. What gets people tickets (rarely) is that the states don't ctrl+a, ctrl+c, ctrl+v the requirements, so some don't get added into the state codes, and they can add on stuff. One example off the top of my head is the third brake light. Federally required after, oh, 1984 I think, but not required in my state. The cops can't stop you if it is completely removed and made to look as if it was never there, but they can stop you if it is broken, because the statute reads that way. For the opposite example, I think we regulated the ground-effects lighting recently.
:(
carefully tucks my silver hair into a hat