I have to wonder if a someone whose family has been in Canada for a few hundred years would get in a snit if you called them "Canadian"? Or if someone whose ancestors came to Australia in the 1800s would get indignant if you called them an "Australian"? Hmmmm......Somehow, I don't think so.
I have a friend whose family came to Texas from Germany over 150 years ago and did nothing but marry other German-American immigrants from then on. Her last name is Kaiser....That's how German she is.

If she started insisting she was German instead of American, people would roll their eyes.
We can agree to disagree, but I say common sense dictates that if your family has been in Mexico willingly for a few hundred years, then you are as Mexican as Mexican can be. I won't get into it, but anyone who grew up in Texas is all too aware of why some "Spanish" Mexicans might get huffy about being called Mexican. It's essentially a caste system. I'm not going to be a defacto part of that system by catering to someone who refuses to refer to themselves as "Mexican" because that would associate them with their fellow "inferior" countrymen. It's the worst kind of classism. So I do understand it. I simply won't acquiesce to it.
They may not be mestizo, but they ARE Mexican. They can be a Mexican of Spanish descent and still be Mexican. Again, I maintain that if being called a Mexican makes someone from Mexico THAT uncomfortable or even downright upset, then they are the ones who have a problem internally with their own country. It is not MY problem and I commit no offense by calling a citizen of Mexico "Mexican." If they are offended by being identified with their own country, then they need to head back to Spain, where they can hold their heads high.....if they can swing it with Spanish immigration.
If someone's feelings are hurt by me stating a fact, then I will not bow to such silliness. Good heavens, I have plenty of Mexican friends (and yes, they're the "Spanish" ones) who say without hesitation that they are Mexican......because THEY ARE. They didn't come here from Spain; they came from Mexico. It's a fact, not a slur.
I'm in Texas.....If I went around asking everyone from Mexico, "Would you be offended if I called you a Mexican? What would you like to be called?" most of them would think I was a lunatic, and plenty would be offended that I even ASKED such a question, because the very question implies there might be something WRONG with being called a Mexican. So if they're proud to be called "Mexican," I have just insulted them. ACK! I know my reaction probably wouldn't be positive if someone asked me if I minded being called an American.

So "just asking" what they want to be called can itself be like stirring a hornet's nest, and for no good reason. Maybe I would stay on the good side of the person who resents being identified as a Mexican when they're from Mexico, but I'm pretty sure I'd wind up offending many more people who would think to themselves, "What does she mean...do I MIND being called Mexican? WTH is wrong with being called Mexican???"
No thanks. I'll stay on the good side of the reasonable Mexicans.