My experience is very different because I've never been in a deep red or rural area, and I'm a young-ish white male who presumably doesn't look poor.

But anecdotally, I've never been stopped walking or running anywhere. Occasionally but rarely someone honks or yells out something obnoxious out of a car.

Sidewalks are surprisingly empty though, even in urban areas. Even in Boston, the "third most walk-able city", there are a lot of beautiful places where you just don't see many people.