It seems that you have a specific dislike for a certain culture, irregardless of their immigration status. You’ve basically said yes to the question posed by the OP.
I imagine that South Texas would drive you crazy since it is full of Hispanics with ties to Old Mexico who have always been US citizens (in a good part of the past century they were 2nd class citizens because the people in political power felt like you and did something about it).
I’ve lived in NM and TX my whole life and have never seen some entrenched Mexican nationalist movement in politics except a minority of nutcases in South Texas. Both states are full of Hispanics, including “Mexicans.”
I don’t see how respecting one’s heritage, including county of origin, is an automatic disloyality oath to the country that one resides in. Even some big time players in this country have dual citizenships such as Karl Rove.
If we cease to tolerate different cultural aspects of the citizens of this country, we become less free. I see that certain aspects of my culture (gun ownership, hunting, trapping, rodeos, cock fights, horse races, etc.) are under fire and in danger by those that feel culturally superior to me. I couldn’t bring that fire and danger to another’s culture when that culture doesn’t take away any of my freedoms.