We spent a few days in Valentine to visit Niobara Scenic River(not worth a special trip). Did not know that it was a Reservation. Over the years we've been on and thru many reservations and mostly never noticed especially other than a sign or two. Once we had a problem, there was some political fracus going on and some hotheads (Wind River area) yelled at us but that ws back in the 1980's and didn't amount to anything.
Some reservations have special rules, the Navajo comes to mind, but just check before you wander off the main roads or try boondocking.