I think that the problem is more complicated than you're phrasing it. An insult like "likes fried chicken" is the dog-whistle of racism - most of us hear a fairly harmless statement, but folks with racist tendencies hear a whole host of stereotypical associations with black people being poor, low class and unsophisticated. It's a simple statement, but there is hostile intent there in a lot of cases.
I agree that the victims of these sorts of insults should avoid giving the bigot any satisfaction by geting worked up, but somebody's gotta say something. As well as intending to get a rise out of someone, bigots say things like this looking for silent agreement from "their kind of people", so let's take it away. Openminded white folks have to be right in there challenging these statements, so that minority groups don't feel like they're the only ones that see a problem.