Having read the piece you linked to... Do some tribes believe the word "Indian" is horrible and derogatory because I know my friend got that impression from a Native American.
If the person claiming to be Native American looks as White as you or I, is it still wrong to ask "how much"? Would a Native American not ask?
"Indian" term dying out?
"American Indian" vs. "Native American"
Canadians dislike the term "Indian" for some reason. Liberals who think they're being PC sometimes prefer "Native American." A few Indians disdain the term "Indian" because they consider it a mistake. But the vast majority of Indians use the term "Indian" to describe themselves. It's perfectly acceptable in polite society.
Asking "how much" is about as impolite as asking any personal question. You can do it with someone you know, but not a stranger.
It's complicated by the fact that membership in a tribe is a political decision, not a biological one. It's just like citizenship in any country. If a tribe says you're a member, that makes you an Indian. Even if you have little or no Indian "blood."
For more on the subject, see:
White man leads Indian tribe
Are pure-white Indians possible?
"Actual Indian" defined
The immigration question
This led to a more interesting question: If allowing immigrants to become citizens is good for the United States, is it also good for Indian nations? Why don't they open up their membership to "immigrants"--i.e., non-Indians who would contribute to the tribes in some way?
But tribes have little or no incentive to do this, since it would dilute the power and wealth of existing Indians. So pundits who worry about this possibility are raising a straw-man argument.
Were white Americans introduced to Native tribes in a large scale, the main issue I see would be a dilution of tribal identity which is largely the purpose of being politically independent in the first place. The immigration I believe would enhance power and money: white tax resisters tend to have money to resent being taxed, often are business owners, and wield political power simply as a function of being white in a racist USA.
Tribes have a finite amount of land and receive a finite amount of treaty benefits from the government. Unlike a US city or the US economy, these things aren't easily expanded.
The value of immigration comes from new ideas and energy, not from raw numbers of people. Tribes are already interacting with the rest of America and getting new ideas and energy.
In fact, two-thirds of Indians live off the reservation these days. So Indians themselves act as the bearers of new ideas and energy. They don't need outsiders moving onto their land and diluting their cultural and financial resources.
Interaction is good
True, some tribes have been too insular in the past, but that's starting to change. Gaming, tourism, and other businesses are forcing them to deal with the outside world. So is the Internet and other new media.
This changing environment is causing effects equivalent to immigration. Because of Twilight, the Quileute tribe has begun promoting its arts and festivals to fans. Because of Losing It with Jillian, the Yavapai-Apache Nation now has access to fitness trainers and online health plans.
Controlled access to the mainstream is good. Uncontrolled access would be bad. The US has some 300 million people, so 10 million immigrants won't seriously harm its culture. A typical tribe might have 3,000 members, so 100 non-Indian casino workers wouldn't seriously harm its culture. But non-Indians have the potential to dominate or overwhelm a tribe, so letting people in is problematical.
Your white tax resisters would add the wrong kind of power. They'd seek to control or dismantle tribal governments, not support and enhance them. Tribes don't need that kind of "help."
They also don't need criminals who would use sovereignty as a shield against prosecution. Or speculators who would try to buy or sell their land. (Been there, done that.) Or wannabes who would turn their religious rites into self-help seminars.
Most Indians are already "living in two worlds." Education and jobs are tugging them away from the reservation. Family and cultural ties are tugging them back to the reservation. They can decide for themselves if more access would be beneficial. They don't need wise guys like us telling them to open their lands to immigrants.
For more on tax resisters, see Anti-Government Extremists Pose as "Indians"and Self-Proclaimed "Indian" Secedes from City. For more on the subject in general, see Should Indians Cling to Reservations?