There's a reason for people to hate it... it's a tool used for something similar to genocide, only instead of killing the individuals (like they did in the past) it is used to reduce the population out of existence over time. To get benefits as a tribal member, you need to have a blood quantum over a certain amount. That means native populations are guaranteed to shrink because there are fewer and fewer 'full bloods'.

It's also incredibly racist, when you get down to it. Does a white person need to be able to trace their lineage to claim they are white, or any other race, for that matter?

When you talk to Cherokee people, most of them are very clear that if you are part of the Cherokee culture, you're Cherokee. Throughout history, they have 'adopted' people of other races into their tribes, and those people married and had children. If an adopted white man married and adopted white woman, their children would be considered full blood, regardless of their skin color. So from a Cherokee perspective (and I assume any tribes that behaved similarly) the measure of a Cherokee is whether they are a part of the Cherokee culture, rather than what their genealogy shows.