Answer
Because the Constitution vested the Legislative Branch with plenary power over Indian Affairs, states have no authority over tribal governments unless expressly authorized by Congress. While federally recognized tribes generally are not subordinate to states, they can have a government-to-government relationship with these other sovereigns, as well.
Furthermore, federally recognized tribes possess both the right and the authority to regulate activities on their lands independently from state government control. They can enact and enforce stricter or more lenient laws and regulations than those of the surrounding or neighboring state(s) wherein they are located. Yet, tribes frequently collaborate and cooperate with states through compacts or other agreements on matters of mutual concern such as environmental protection and law enforcement.