Assuming that "twitter"-ers can choose who they follow and whose "tweets" they see, it seems to be an issue of what you choose to look at on twitter. Undeniably, anyone can come off as ignorant; regardless of race. Certainly there are specific cultural trends the African American community may tweet about avidly, but this is not to be differentiated from the same way the stereotypical, white, middle-aged woman would tweet about her love for John Mayer.
In regard to the children exposed to this content, there's nothing we can do. The internet has opened quite an infinite gateway of information for young people. By going through google, a simply combination of words and click of a mouse can bring a child to racist, inappropriate, and/or offensive material. Pornography, hateful words, crude humor, it's all there for them. Trying to shelter children from the real hate and ignorance of common people is not the answer, instead we must teach them not to think in the same manner.