In the American context, racism is a system of institutions, attitudes, and ideas which preserve white power and privilege. In other contexts, racism is any system of institutions, attitudes, and ideas which preserve the power and privilege of certain large social groups, defined on the basis of birth, kinship, or more often notional kinship. Racism is not defined by skin color. Racism can target linguistic, religious, or other cultural groups.
If we are going to stop racism, we must challenge racism, racist ideas, and racist mindsets. We need to start with ourselves, and recognize our internalized racism, in order to escape from it.
(I admit I don't have any direct experience of racial oppression. I make an analogy between racism and sexism, and draw on my experience of sexism to try to fight racism too.)
Nativism disproportionately hurts people of color. So nativist institutions and attitudes reinforce white supremacy. A law need not mention race to be racist. For example, many states required literacy tests in order for people to vote; these literacy tests were used to keep people of color from voting. A law can be racist because of its intent, context or application.
Nativism calls for the supremacy of the native-born over the foreign-born, and for discrimination on the basis of where people were born and who they were born to. So it is rooted in the same mindset as any other type of racism.
Edit: To clarify, I'd like to distinguish racial prejudice from racial oppression. Both of these have been called racism, but, in this diary, I'm referring to racial oppression, not prejudice.
Racial prejudice is an individual vice, of seeing someone as less, because of their skin-color, language, nationality, etc. I think we should try to untangle racial prejudice in ourselves, but the important thing is to end racial oppression.
Racial oppression is when social institutions deny some people, because of their skin-color, language, nationality, etc. the human rights, the opportunities, and the respect that other people may take for granted. In some cases, it is more fluid than in other cases, but it still shows in wage gaps and other results.