Yes -- and what ethnic terminology such a person would prefer to use is a complicated and delicate issue, and I think you should call them whatever they want to

Yes -- and what ethnic terminology such a person would prefer to use is a complicated and delicate issue, and I think you should call them whatever they want to be called (within reason). But I certainly wouldn't suggest listening to the opinions of random Anglos who aren't affected by the issue at all claiming that "calling someone Mexican is offensive"