If you look at early American history, Americans were not classified according to race.
Instead, we were Germans, French, English, Dutch, Swedes, etc.
We don't even have to look back that far. Just 35 years ago, Americans were still identifying themselves by the homeland of their ancestors. Today, they call themselves white because their ancestors intermarried with so many other people of European descent that they cannot trace their ancestry back to a single country. The term white has always been a subjective one, and "white" was never a culture. This country has always been a melting pot.