How do legal classifications of roads (e.g. Interstate, US Highway, SR, etc.) affect rights?

The MUTCD is adopted, in part or in whole, by various states as they see fit. Oregon, for instance, has its own unique speed limit signs. The MUTCD is not a statute.

Under our Constitution, the federal government simply lacks the power to prescribe rules regarding such things as mailbox posts or blinker usage or texting while driving.

Another thing: if it’s not covered by local zoning, the agency controlling the road establishes access management standards, or the number, location and configuration of driveway or access points. “Continuous access” or “continuous curb cuts”, where there’s no differentiation between the road and a parking surface next to it, is now illegal in many places.

If you’ve ever been to Arkansas, (or, if you live in Arkansas, ever left the state), then you know the state handles most of the roads. Say you come to Arkansas from Missouri. The second you cross that line, the roads will become a lot bumpier. If you look, you can even see the vast quality difference.