I'm quite sure that a national park would not be allowed to set different fees for residents of different U.S. states--the federal courts would rule against such a discriminatory step.
State parks, of course, can charge more for nonresidents who don't pay taxes to that state. Many states do not do so because they are dependent on out-of-state tourism.
Technically, national parks could charge more for tourists from other countries, who do make up a significant percentage of their visitors. I suspect that the additional personnel needed to check everyone's ID or passport would offset any extra income!
May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey