The Republicans have made it clear enough that they are going the arch-nativist route.
Exactly. "No one asks to see my birth certificate!", "self-deport" etc sent the clearest possible message that non-white immigrant communities' votes are not welcome.
It has an equivalent of sorts in the "war on coal", by the way.
Just one little flaw in your imaginary "big bad GOP racists" theory, most Cuban-Americans are white.
That's true by any reasonable standard, but race in America is very weird in this regard.