Perhaps the problem is pretending that everyone is the same. The kids aren't stupid, they can see this isn't true, and they're bound to fill that vacuum with whatever else they can pick up.
I'd think that the better strategy would be to embrace the difference. Recognize that races and cultures really do have different qualities. But because the mixture is so complex, and the world that we apply those qualities within is also so chaotic, that it's quite impossible to say that, in the final reckoning, any one is superior to another.
The better strategy is to explicitly acknowledge observable differences - skin colour, accent, etc. - and point out that those things don't tell us what kind of person someone is.
One of my favorite examples here is that a good portion of African-descended people have a resistance to malaria, which is certainly relevant to ones life in tropical climes. And on the other hand, those same people are susceptible to sickle-cell anemia.
The ability to digest lactose comes from a genetic mutation that's been traced down to northern Europe; most other people don't handle dairy well (sorry, don't have a handy reference). This may not be a big deal, except to the person having diarrhea because his friend assumed that everyone's digestion works the same.
Differing climate and lifestyles has led to physical characteristics differing in lung capacity, amount and distribution of musculature, etc.
[Edit: my characterization below of Chomsky's position is backwards, he opposed this idea]
Noam Chomsky posited that, much like computer languages, the language that a person speaks influences the way he thinks, and more recent research tends to support this. As a result, some people are better equipped mentally for different tasks. For example, there's a group in New Zealand that has no "relative direction" words like "left" and "right"; instead, all of their directional communications are in absolutes ("North", "West", etc.). Somehow they are far better than others at maintaining a sense of direction, so for any task that requires such a sense, these may be the best candidates.
It's probably not mere chance nor prejudice that some groups are better or worse represented in professional sports. For whatever reason, there's a preponderance of Africans and paucity of Asians in American football. I find it hard to believe that football coaches are being racist when there are such huge amounts of money on the line.
People really aren't all the same. We have differences, and in many cases those differences are shared within demographic groups. Why do we want to pretend that this isn't true, rather than reveling in special opportunities that it affords all of us?
Addendum: I realized that I partly answered based on culture (language) rather than race, as you asked. This points to a bigger question: what is race? Are the peoples of southern Europe separate from the northeners? Archaologists generally believe that American Indians are descended from Asians crossing the Bering Straits; should we view these as the same race, or separate? I'm not trying to be provocative, I really don't know how to define this.
I sort of tackled the "what is race" question in another comment. [1] I kinda agree with you on culture is important, but I find that generalizations there fall flat, as subcultures within a culture tend to contradict each other. In all cases, the fundamental fallacy of bias comes from using attributes associated with some group to make decisions about an individual, who may or may not share those attributes. Our brains attempt to create heuristics for us, we have to actively work to supplant them with logic.
I'll now proceed to go off on a tangent from something that's already just barely topical for HN...
Our brains attempt to create heuristics for us, we have to actively work to supplant them with logic.
I generally agree with this. The benefits of civilization make most of these heuristics unnecessary, and more of a liability. But I wish that people advocating this would see its application in further areas.
In his The Fatal Conceit, Hayek talks about how our evolution within small tribes gave us the instinct to be compassionate with others, but that in today's wide world, that instinct just can't scale far enough. This is another area where we need to reject the emotional reactions that are pre-programmed into our brains, and think more rationally about whether what the little voice says really makes sense.
I'd think that the better strategy would be to embrace the difference. Recognize that races and cultures really do have different qualities. But because the mixture is so complex, and the world that we apply those qualities within is also so chaotic, that it's quite impossible to say that, in the final reckoning, any one is superior to another.
[Edit: dropped "up" at end of 1st paragraph]