Maybe we should talk about this in terms of "passing," or the idea that some people can "pass" as white, or not-brown and therefore are treated differently than people with darker skin.
So, Haley can pass as white when it's convenient, but can also identify as Indian when it suits her. The idea of passing has been around for a long time, and goes into the Spanish empire's own structure of race, which essentially classified people in degrees of being Spanish, i.e. white, and being mixed with indigenous or African peoples. In the late Spanish empire, people could ask the church to reclassify them, and lubricated by the right amount of gold, the church would often agree, effectively changing someone's race. This is in part still supported by class in Mexico, where people with light skin and blue eyes are often in the aristocracy in Mexico City, while darker people are poor, and often in the south down in near the Yucatan peninsula.
From the U.S., they're all treated as Mexicans, but the people from Mexico City could immediately pass as white, while those from indigenous areas in the south will still be considered brown, even as both are Latinos.
Haley can pass, but also be a "brown girl." One of the things that's weird is that she talks about being a brown girl, argues that the U.S. is beyond racism, and yet, Nimrata still calls herself Nikki.