What's funny is that in South Texas in particular those folks with Mexican roots can be very particular about it. Some label them Mexican-Americans, some Hispanics (which some folks with Mexican roots despise), some Latino, some Chicano, etc.....
Most of the time it's the folks that insist upon being referred to as Mexican or Mexican-American that are the most outspoken. I'll ask what city in Mexico they were born? Their answer, "I was born in Texas". I'll ask what city in Mexico their parents were born in. Their answer, "They were born in Texas." I'll ask what city in Mexico their grandparents were born in? Their answer, "They were born in Texas." I'll ask what city in Mexico their great grandparents were born in? Their answer will either be,"My great grandparents were both in [random city in Mexico]," or "my great grandparents were born in Texas, but my great, great grandparents were born in [random city in Mexico]."
Summary, aside from their great, great grandparents everyone else is an American. Not a Mexican. Not a Mexican-American. Just an American. I've never filled out a job application with "German/Irish-American" because my great, great, great grandparents were born in Germany and Ireland LOL.
Basically, the term "African-American" is meaningless for the vast majority of blacks unless they themselves were born in Africa. And even if they were born in Africa and became American citizens they are now Americans. Enough of this hyphenated "[blank]-American" stuff. If someone is born in another country and has dual citizenship in the country of their birth and America and maintains a permanent residence in both countries then use the hyphenated name thing

. From what I understand though, the laws of dual citizenship in most countries are very restrictive and selective (I can't speak to it in any depth).
For me the issue is borderline pretentious nonsense.