I see race as the most important of those barriers. Language can be learned. Cultures change all the time and the next generation will usually be assimilated anyway, if they are of similar ethnicity. Race on the other hand is an unchangeable part of us.

However much people want to believe in color blind societies they just don't exist. People understand race on primal level and treat people differently because of it. This can be seen in practically all multi-ethnic societies. Different ethic groups overwhelmingly marry people of their own kind even when they have culturally assimilated into the wider culture. The single best predictor of voting behavior is race, not for example class. Rich and poor whites vote mostly for Republicans and all nonwhites vote overwhelmingly for Democrats.