Language Problems

A writer posed a question in one of the Linked In groups I'm a member of asking if he, as a white guy, would be seen as racist for featuring a black female character in his work who used a lot of slang and ungrammatical speech. I understand this man's hesitation in writing anything that would appear racist or derogatory toward any group, but I also think characters need to be who they are. Some people speak the King's English and some don't. Writers should be free to write the voices they hear in their heads.