Not really, though that's a pretty broad topic. Obviously there's some xenophobia in Japanese culture, but that's fairly normal. The Japanese may dislike the South Koreans, but there are elements of American culture that dislike Hispanics. Japanese WW2 vets may dislike Americans, but there are American vets who feel the same about them. As a whole I would say no, at least not intentionally. Obviously they have a more homogenized society, but I haven't seen anything in anime that shows a clear dislike of other races. The worst I've seen are some of their old fashioned depictions of black culture, but they don't have the history of persecution we have, so they don't necessarily see certain images as racist in the same way we would.
You could make a stronger case for sexism, though even this only represents certain parts of the culture. The same can be found in aspects of American society (like in some comics). Miyazaki is the biggest feminist around.
