>It's weird because I have friends who are clearly of native American decent, who's kids are clearly of native American decent and they can't gain membership to their associated tribes but my family all has their membership through an ex cheif from the 1800s of one of our tribes here and we're what I can only describe as Caucasian.

The reason for this is that blood quanta is not how most tribes historically determine membership. Various tribes used either matrilineal of patrilineal descent where if either your mother or father but not the other was part of the tribe then you had a place in their matrineal or patrilineal clan systems, which is to say part of the tribe because the clans were the basis of the tribe.

Tribal membership rooted out of clan membership, if you had no clan you were basically an outcast to the tribe because you had no place, as your clan is what made your place. The political systems revolved entirely around this, in a matrilineal tribe like the Iroquois you would have clan mothers who were like your mother's mother and anyone descended from them was part of that clan and the various clan mothers made a tribe as each clan mother ruled over a longhouse and multiple longhouses made up the village. If you had no clan mother you had no longhouse so you were not part of the village etc. Now the men would still rule usual, but they did so by way of their maternal descent and it was a big taboo to go against your clan mother even if you were the high chief or whatever.

Of course what I am saying is not universally applicable as it is only applicable to the group I am basing it off of, as obviously patrilineal tribes also existed who would be more like Arabs where if your father is an Arab you are an Arab regardless of who your mother was and this extends backwards indefinitely such that you have berbers in north africa who claim to be arab despite being not remotely arab simply as a result of (likely forged) genealogies. In such an analogy various arab "tribes" are more like clans, as several tribes made up the arabs as a whole but you get the idea. The specific name and level of the word used to describe what I'm talking about is irrelevant.

European "dynasties" were obviously a thing and worked similarly but they didn't really make it across the Atlantic so a new system basically rose up where male and female ancestry was weighted equally called blood quanta where you were "half" regardless of if your parent was male or female. I think this was influenced by the fact that they had to deal with confusion arising from having some groups being patrilineal while others were matrilineal so they just created one system to cover both as an attempt to understand why it sometimes worked and sometimes didn't, because otherwise you would have to track every native group individually based on their own rules.