In 1978 the daughter of Julia Martinez, a full-blood Indian from Santa Clara Pueblo, was denied tribal membership because her father was not of Santa Clara descent and sued the tribe in the Supreme Court. Santa Clara Pueblo has always determined its tribal membership based on paternal descent; one must have a father who is an enrolled tribal member in order to qualify for membership (citizenship). In Santa Clara Pueblo v. Martinez the Supreme Court affirmed the right of Native American nations to determine their own citizenry (i.e. tribal enrollment rules). It was an unfortunate blow to the Martinez family, but the case is widely regarded as one of the most important decisions that upholds tribal sovereignty and restricts the federal government's ability to interfere in internal tribal matters.
The Cherokee Nation has been the center of controversy and a challenger of the United States since at least 1823 when it brought its first case before the Supreme Court. The same is true today with the ongoing Freedmen issue (this week on the Native American history page at About.com in the Tribal Profile section I have featured the Cherokee Nation and briefly covered the topic there). The issue of the Cherokee excluding black descendents from its rolls raises troubling questions about racism and a tribe's right to decide its own citizenship; in a nutshell, should a tribal nation have the right to determine its own citizenry even if its rules appear to be racially discriminatory? And more importantly, should the United States have the right to interfere with whatever those rules are (which they have done in the Freedman case)?
There is no simple or easy answer but one thing to keep in mind is that nothing any tribal nation does today exists outside of the history of colonization; that is, the history of the United States' continual interference in tribal matters. In other words, from a post-colonial (or neo-colonial) perspective this is a matter of questioning the wisdom of expecting a colonizing government to continue to intervene in the internal matters of a sovereign nation.