For the purpose of a discussion about diversity, I think the more important measure is how they identify themselves culturally. Being able to genetically trace your roots to the mayflower but being raised steeped in Mexican (to avoid the term in question) culture (for example, adopted) would still yield more diversity, by the definition we are usually using when referring to national diversity (which I think is generally interpreted as cultural diversity of a nation).

They're not considered white by the locals until they lose their accent. White is what you're considered by the relevant whites under discussion, not a meaningful physical category. Mediterranean-bordering, Irish, and Slavic people have just gotten to be white in the US fairly recently.