There is no Native American religion in the way there is a Lutheranism or a Theravada. There are the religions of the Dine, the Lakota, the Hopi, the Haudenosaunee, the Tlingit, the Yupik, the Anishinaabe, the Muscogee and several hundred more, in unrelated language families, with different creator accounts, different ritual specialists, different calendars and different relationships to their neighbours. A Haudenosaunee Longhouse ceremony and a Hopi kachina cycle are not two versions of one thing.
The category exists anyway, for three reasons worth naming. Outsiders invented it, because colonial administration needed one word for everything it was not. Federal law then made it real: the same statutes that criminalised ceremony in the 1880s and the same statutes that protected it after 1978 applied to all these nations at once, which gave them a genuine shared legal history. And Native people themselves have at times organised across nations, in the Ghost Dance, in the Native American Church, in the American Indian Movement, producing real pan-tribal forms.
The failure mode is pan-Indianism: taking a Lakota pipe, a Dine sand painting and a generalised Great Spirit and presenting the composite as what Indians believe. That composite is not held by anyone. It is also the version most often sold, and its circulation is a live grievance, since the specific traditions it borrows from are frequently closed.
Two further cautions. Many of these communities do not use a word equivalent to religion, because the practices in question are not separable from kinship, hunting, farming and law. And a great many Native people are Christian, or Christian and traditional at once, without regarding that as a compromise.