It has become common practice to ask the race, or culture of someone else. Many times people have turned it into a game. Sitting in class on the first day of school, introducing myself two seconds pass after I say my name that I'm asked what nationality I am. The person next to me begins to guess, Mexican, Puerto Rican and sometimes even Indian.
I don't find it offensive or intrusive, because we no longer live in a world where cultures must assimilate to one, but we celebrate our differences. Being Latina/Hispanic/Chicana/Mexican-American describes me. However, many women find the "title" offensive.
Eva Mendes has explained on interviews how she does not see herself as Latina, but as an American. The new kind of American girl. Although, I see how she doesn't want to separate herself from the American culture, being of Cuban origin, I don't see the harm in embracing your roots. Does checking the Hispanic box on a survey make you less American?
Living in the U.S. makes us unique individuals, because we live in a melting pot of cultures. There is no shame in proclaiming your culture, living in this country makes us Americans. Not living a certain lifestyle.