Very good question! It should be obvious that any form of racism is against the Torah. It is forbidden to use derogatory names to refer to individuals, so of course it also forbidden to refer to racial or cultural groups in such a manner. It is also an aveira to hurt anyone with words. And we are supposed to judge everyone favorably, and learn from every person (Avos). Don’t despise anyone, since every person has his hour (Avos.)
This is a very important issue, since for the vast majority of Americans and people in other countries, it is obvious that racism is wrong. So it is a huge chillul Hashem when any frum Jew says or does anything racist. Being non-racist is part of what “derech eretz” entails now. If we want to be a light to the nations we have to abide by the minimal standards of decency of society — and then to show non-Jews that the Torah allows us to go beyond derech eretz and be even better people.