This is an interesting question, but I will suggest that it might be revised to place the responsibility to provide civil rights on the United States rather than on the American Indian.
From 1865 until late in the 20thC, one can argue that the United States' policies toward American Indians actually precluded them from acquiring civil rights. For example, the creation of the reservation system during the Indian Wars and after, effectively segregated the largest percentage of American Indians from the rest of American society, almost guarantying that the issue of civil rights on a cultural scale would never be seriously discussed or acted upon. To the extent that the American Indian was accorded civil rights until relatively recently, it was done on a exception basis and reluctantly.
Historians and sociologists have argued for a long time about what the reservation system has done to American Indian culture, but there can be little doubt that when the segregation of a group becomes institutionalized, as it has been with American Indians, the issue of whether that population has true civil rights almost becomes mute because they cannot exercise their civil rights as fully-integrated members of the general population of the United States.
The argument has been made, of course, that American Indians are free to join the population outside the reservation system, and tens of thousands have done so over the last century and a half, but the reservation is set up to disincentivize people from moving away--in part, because they are then leaving a very unique culture in which they feel respected, understood, and insulated from a culture for which they most likely have no affinity. Some critics have argued that staying "on the Rez" is a symptom of the American Indians' reluctance to join the larger society, and that is undoubtedly true for many people, but that is a minor part of the overall problem of exclusion that American Indians have suffered since the early 1800s.
In sum, then, although there are legitimate arguments that American Indians have contributed to the lack of advancement of their civil rights, there are many stronger countervailing arguments that the American Indian has never had the opportunity to enhance access to full civil rights.