It's handled by individual tribal governments. Some are very strict about who they let in, others are much more liberal about it. Basically it isn't our federal government that makes that determination.
Just below you somebody posted that Barker was of 1/8 Native heritage.
Yet he grew up on a reservation, and even strict tribal elders should (and probably did) take into consideration Barker's positive accomplishments for society in general, such as his campaign of awareness to spay/neuter pets to help keep the population under control humanely, and he was never afraid of using his microphone and airtime to remind his large audience every day, for decades.
What I'm saying is, even if 1/8 wasn't technically enough, he could have made it in just like accomplished artists often receive honorary PhDs from prestigious Universities, even when they did not have (or finish) their formal education when younger.
57% of which tribe? With more than half, I would expect you to have a fairly strong upbringing in the tribe with various customs and your parents likely know how to get you enrolled.
Not always that simple. My father has tried for years but gets stonewalled because of who his father was, my grandfather was disowned for marrying a white woman rather than leave her a single mother. In the end I think being cut off like that is what killed my grandfather really.
Some tribes have been in legal battles over the past few decades because they're trying to disenroll people no matter how "native" they are. IIRC at least one tribe was limiting membership to only the descendants of the families that signed a specific treaty and then only if they had the paperwork to back it up. Which, if you know anything about the history of natives in this country, is really fucked up to require.
Not the one I remember but here's an example of a tribe disenrolling people regardless of their "blood quantum":