Each tribe defines membership for itself. It's not a question of whether you think you qualify under those membership rules but whether the tribe agrees that you qualify. You are free to apply for membership, but many who apply are not accepted. Indeed, many one-time tribe members get cast out during periodic purges.
As usual, Republican commentators appear to be exceptionally ignorant about the mechanics of how affirmative action categories work. This is a topic that demands vastly more attention than it gets from Republicans. As a notorious raving extremist, I'm always counseling that we should attempt to understand where all sides are coming from in the major long-term arguments. For example, is race a biological phenomenon or a social construct? Well, it's both, and it's important to grasp the precise reasons for it being both and how they apply to each group.
In determining the future of the country, the usual issues of the day, such as the estate tax or whatever, aren't really that important. The real drivers of the future will be how many people are in America, who they are, and who they think they are. Only the last of the three questions is considered at all proper to bring up in Republican circles, and even then it's kept on this woozy level of how people ought to feel, with little discussion of how government policy influences how people feel about who they are. And the notion that government policies could be adjusted for the long-term benefit of the Republican Party is almost wholly alien to Republicans.
When Republicans do talk about how the government defines race and ethnicity, the level of insight is low, typically based on wishful moralizing about blacks. You'll see assertions that black people only feel black because the government gives them affirmative action for saying they are black. Most people recognize that as a pretty stupid argument, and since few whites care about anybody other than whites and blacks, the fact that this line of thought is less stupid when applied to Hispanics or to South Asians being counted in with Chinese never ever dawns on Republican "strategists."
Hence, almost no Republican critics of Warren fathom what exactly she did wrong.