How is race used to define who is American? How is race used to define who is American?
I would argue that race is no longer used to define who is American except among a very small number of extremists. Nowadays, the assumption that a white person is more American than a non-white person is vanishingly rare.
In the past, being American was clearly tied to being white. Blacks were excluded from full citizenship for a long time. Asians were excluded from the country (Chinese in the 1880s, Japanese internment in WWII, inability of Japanese-born to become citizens before that) or from equal citizenship as well.
The average American is still a white person as whites are still the majority of the country. But being American is no longer identified with being white. We live in a country where the President of the US is half-black and two Republican governors in the South are from the Indian subcontinent. One need no longer be white to be American. (I, myself, am only half-white and don't even look white at all and I have rarely felt stigmatized on that ground.)
I would argue, then, that race is no longer used to define who is American. We do still privilege white skin and white culture (however that is defined) to some extent. The prototypical American may still be defined as white. But race is no longer a bar to being truly American.
Americans are of all races, but I think most people picture caucasions. It's just the majority image historically. However, America is also universally known as a melting pot. Anyone can be an American, and that's what makes our coutry unique. After all, our president is black!