I think that the racialization of Hispanics as a group has been pretty bad for "non-white" Latinos too.
1. You are right that someone that doesn't visually appear "white" will be racialized in the US. However, the magnitude of this racialization can differ a lot. Incessantly repeating that "Hispanics" are a very consistent group of people makes the "otherization" of all Hispanics worse, including for "non-white" ones.
2. Including people of European descent in a group that is going to benefit from affirmative action opens an obvious loophole. Unconscious bias will provoke that the opportunities created by AA end up with people who look/are white, not to Latinos "of color". Hollywood is particularly terrible on that: with most of Hispanic actors looking European (Ana de Armas is a recent example) or coming directly from Europe. I guess they can't find non-white Latinos in LA. ¯\_(ツ)_/¯
3. Finally, the idea of Hispanics forming a genetic cluster will be pernicious for all Hispanics, particularly when applied to medicine. It puts our lives in unnecessary danger.