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!