The remedy for this is to simply ask a white person, "imagine if you were black" and then explain some of the bullshyt you have to deal with on a day-to-day basis growing up, images seen in the media, the way you're treated in school and by authorities, low expectations given to you, and the negative stereotypes. Then again ask them, "imagine if you were black." You will see it in their faces, the lightbulb going off. After that, they usually get it.
Most white people don't ever think about black issues or what it feels like to be a non-white person simple because they don't need to in order to go about their lives in this society (meanwhile a non-white person NEEDS to understand white society to some extent to succeed in it, plus we consume their media so that understanding is ingrained in us from an early age). Their culture is the dominant one, so if they ignore everyone else, they can still be okay, go to school, get a job, etc. They aren't practiced at being truly empathetic with the plight of others. So in knowing this, whenever I'm around a white person who says something ignorant based on a lack of cultural understanding and empathy, I don't get angry, I calmly draw them into a discussion and ask, "imagine if you were black." I've found this approach to be highly effective, and it works wonders.