This has been an issue for generations, and not just with people from Mexico. I'll give you an example.
In 1927, a young couple from Kiev moved to Canada and started a family. Granted they were legal immigrants, but follow along for a bit. They built up a farm out of the worst land possible because it was cheap and no one of "Canadian" desent wanted it. They raised their family in peace, but were still the "dirty Pollack family" (which is even more ironic seeing as they were Ukrainian, not Polish.). When WWII started, all their sons who were of age (or close to) enlisted. Two of them died in combat, but the family was still, to the "real" Canadians just dirty Pollacks.
This is my family's history. The moral of the story... being born somewhere doesn't make you a better citizen and some people (like those who spit at my family no matter how much they worked) don't deserve the place they have as citizens.
Granted, the war that is going on now is a little different than WWII, and the situation for the people from Mexico is far more complicated, but the feelings of the "citizens" seems the same.
Would it matter if these men were to fight for the USA? Probably not. They'd come back (God willing) and still be the "Dirty Mexicans".