I am white, one of my daughters is AA and the other is mixed. My girls are old enough that we have discussed this issue pretty much in depth. I'm sorry to say that we have had to deal with some racist people IRL - a little girl down the street, some kids at the park and pool, and some family members. They have been very mature and gracious and recognized the ignorance behind it. They handle it much better than their brothers who are profoundly offended on their behalf.
We celebrate MLK day, listen to the "I Have a Dream" speech, and read/talk about him every year. As one of my girls said to me, "If it wasn't for him and the brave people who fought for civil rights alongside of him, you probably wouldn't have gotten to be my mommy."