Casey, I've found that most Mexican and central Americans don't speak up much about being "simply called" Mexican, although it's a misnomer with possibly mildly racist overtones. Kinda like calling all Asian looking people Chinese.
Depends on the situation.
The markets here, like
Fiesta, are Mexican markets... that also have other foods from central, and even the US. But, they are Mexican markets, because they get most of their income from Mexican immigrants, and "gringos" like me that like what they sell. I can get stuff at
Fiesta that I can't get anywhere else... and their produce department is pure produce heaven.
I have also found that if someone is from a central American country other than Mexico, they will correct you politely. They understand it is hard to tell the difference from a name.
My family lived in Puerto Rico for three years, and I can usually tell the difference between them and Mexican Americans by their accents. Puerto Ricans speak a different Spanish, a more traditional Spanish, and the accent when they speak English is slightly different. The names are often different, too.
Anyway, my point was that we sometimes take the PC thing more seriously than the people we talk about do. I have friends from Mexico, Puerto Rico, Venezuela, and Columbia. With the possible exception of one of those friends, they don't get bent out of shape if someone thinks they are Mexican. But, that guy gets bent out of shape about lots of things.
But, I have spent a lifetime having my last name misspelled and mispronounced. I actually get a kick out of the most ridiculous mispronunciations. People often add a couple syllables to my name when they try to read it and say it. I just correct them with a smile, and if they are embarrassed, I try to make them feel better about butchering my name. I know they didn't do it on purpose.
CD