Are there any laws forbidding hitchhiking through Native American reservations?
I'm not aware of any such laws, except insofar as they are inherited. It's illegal to hitchhike on an Interstate highway (freeway), and that wouldn't be any different. There may be some, however, and you would need to be specific where you are going.
I think you have a more serious problem, which is that most reservations are sparsely populated with at most moderate traffic, and you could be stuck for a long time in the desert.
It is likely to vary from reservation to reservation, so you need to check the web site for the reservation in question. If the answer is not clear from that, you can contact the tribal council or equivalent to ask.
I frequently drive on public roads that go through a reservation. Every driveway and road leading off a public road onto the reservation is marked with its own "no trespassing" sign. I have heard reports of Tribal Enforcement stopping someone walking near but not on the public road. There are areas of the reservation where visitors are welcome, such as the casino, hotel, and golf course, but the residential and undeveloped areas are limited to the members and their guests.
That is probably one of the most restrictive, and other reservations may allow visitors.