There should be no concerns about traveling through a reservation. If you are on a state or federal highway, no problem. Just be courteous to people, treat the residents like you would anyother person living in the state.
It depends on the reservation, some are closed to all outsiders for many reasons, however, most are open to travelers. Many have casinos and welcome visitors. I'm not sure how you would find out if a reservation is closed, but there are several in SD and in the southwest that are closed due to the Covid rates.
Travel through like you would through any community.