I've read online that there are requisites for non natives to live in certain indian reservations. Is this true? Are there indian reservations in United States where you can't live if you aren't a tribal member?
This may be true of the Nooksack tribe, in a sense. There is a category of Indian land known as trust land, which is held in trust by the US Government for the benefit of a tribe (there is also land that is just plain owned by the tribe). A tribe can thus set rules regarding use of the land that they control, which could mean that nobody can live in a particular place (not uncommon). The tribe could rent out land, and the rental agreement could contain a tribal membership clause. This complaint by the Nooksack Indian Housing Authority alleges that defendant is not a member of the tribe, and that the rental agreement requires defendant to be an enrolled member of the tribe. Defendant was disenrolled, and the eviction action followed. Non-member evictions are not the most popular actions that a tribe undertakes, so finding those rules online is not going to be easy.
Tribes were original recognized under treaties. They are currently recognized as "nations". They are not states and have their own sovereignty. e.g. It's complicated.