I try very hard not to be overtly political in my stories. I just had somebody take the time to post a five hundred word comment on how horrible that American South is.
Very often, if you simply acknowledge a problem, readers will give you more leeway.
I'd start off the story (in the first few chapters at least, where some smart aleck in a bar mouths off to the character, and show that the character isn't just a southern cracker. By recognizing that you're aware of the problem, readers will give you the time to show the character is deeper than their preconceptions. If the character simply walks away from the redneck in the bar, muttering to his friends "Those are the guys who give us such a bad name", you may circumvent many of those complaints.
However, if the characters act like rednecks, then you're only playing into the stereotypes yourself. The key is (eventually) revealing the character to be multidimentional.