Your numbers are way off:
* The US is still 70+% white: https://en.wikipedia.org/wiki/Race_and_ethnicity_in_the_Unit...
* The number of undocumented immigrants is much lower than that: https://www.nytimes.com/2018/11/27/us/illegal-immigrants-pop...
* The US is still 70+% white: https://en.wikipedia.org/wiki/Race_and_ethnicity_in_the_Unit...
* The number of undocumented immigrants is much lower than that: https://www.nytimes.com/2018/11/27/us/illegal-immigrants-pop...
Also:
* I don't see any reason to believe nobody has more than one "cultural identity."
* Race is really more about culture than biology too. Maybe less so, but if for some reason you were motivated to come up with some categorization of people based on their biological ancestry, the races that we talk about wouldn't make a ton of sense. When you hear people saying that race is "socially constructed," this is what they're talking about. The Irish weren't considered white a century ago, and it's not like the change came about due to some scientific breakthrough.
The history of the Irish is a good example of how ethnic groups change and assimilate over time.