Is is stripping Native American culture to force them to conform to American society, or was it American society assimilating Native culture? I'd like to understand the argument here if you could expand further on it. Where does the line get drawn then in regards to this? Is it at if you're not a part of a tribe then you have no claim to being Native American?
American society does not so much assimilate Native culture as it abuses it to its own ends. If you are not part of a tribe, you really are not a native, at least in the way Warren positioned herself. Her using a DNA test to prove her "Nativeness" is wrong (as the Cherokee point out). It is erasure of people. Your blood does not necessarily have anything to do with how Native you are.

Elizabeth Warren is a white woman who has lived as white woman, pulling the Native card when it suited her. She has absolutely no connection or lived experience with any Native culture. Her Nativeness is the same "Indian Princess" trope White Americans have been pulling since 1493. It is very insensitive the way this story is being packaged.

Native nations are better to be thought of as somewhere between a state and a country. The sovrigenty of these nations is very important. A blurring of these lines allows for the encroachment of the US and that, historically has not been a good thing. A clear line and identity between the two allows for the nations to more readily bring up the issues that are important tot them. If any white American with Native ancestry (pretty much all of them) could claim to be a Native, it would very much muddle that and drown their voices out.

She "technically" has ancestry that refutes Trump's attacks on her (separate from the question of ethnicity), but that wasn't what Trump was guffawing about in the first place. So it's like fact-checking the bully punching you, "False, I am actually not hitting myself!"
Trumps attack is same kind of racial crap he has doubled down on. Warren is being insensitive though. She literally doesn't hear the voices she claims to be a part of. This is her trying to get out in front of attack ads in 2020. To many Natives this is a lot more than politics. That is what rubs me the wrong way

(Separately, I'm not sure how much I value the right of tribes to enforce racial rules. Ethnostates everywhere probably have to be dismantled.)
I wouldn't call them Ethno-states. The current Cherokee chief has very little "Cherokee" blood. Each Tribe has its own set of rules and frankly I am ignorant on a lot of the finer points of it. I do know I have seen Native people of all sizes, shapes, and colors.