Human beings unconsciously fear the unfamiliar. This is the case even if we've been raised in an environment where we've been taught to treat all people the same. I think a good way to overcome this natural tendency is to make an effort to get to know people from other races and ethnic groups. Maybe you could volunteer with an organization that helps new immigrants get settled into their new homes.
Other than that, if you just treat everyone with equal respect and compassion, I'm sure you'll do just fine!
When I was doing clinical in nursing school, I was amazed by the misunderstandings that could happen just because people didn't speak the same language! One poor lady wound up dosed with haldol because she got frightened when she couldn't communicate with her caregivers, and lashed out at them in self-defence.
I had her as a patient the next day, and found that as long as I took my time and was gentle with her, and used non-verbal cues to show what I wanted, we got along just fine.