I was reading a great book that addressed research on a variety of issues. One topic was discussions about race. Children are often seen as being color blind, but in reality even the youngest children start classifying things into simple categories (like me, not like me). However that does not mean that they are biased in their behavior. That comes as they get older. Even when asked by researchers to address issues of race in discussions with young children only about 10% of white families actually did while 86% of black families did. African-American families often did so as a means of preparing their children for potential racism they might encounter (which also might have sensitized them so that they assumed some things were racially biased that were not). White families just felt uncomfortable with the whole topics and felt that if they didn't know what to say or how to say it they should ignore it.
What to do? Many topics are good for including at an early age. Does your young child have both white and black baby dolls? How about picture books? Are a variety of races depicted? To be effective conversations about race have to be explicit and in terms that children can understand. Even a concept that parents think children understand, they don't at a young age (What does equal mean?) When talking about historical events it is important to talk about the context and to not just brush over them. As children get older talk about their thoughts and feelings and help them to be accepting. If you know stories or jokes that have racial overtones then do not pass them on to the next generation. Make the decision to set your children up to overcome the challenges of prior generations.