As a native of the deep south, I have no problem with southern accents. Of course, there isn't just one southern accent, just like there isn't just one Texas accent. A person from Georgia is going to sound very different from a guy from Mississippi or a person from South Carolina. And if you're from Florida, well, you probably don't sound like anything special at all.
My beef is with how Hollywood portrays the southern accent. It seems their voice coaches basically tell the actors to sound like Elmer Fudd. Sally Field, for instance, as Forrest Gump's mother, seems to follow this advice to the letter. "I'm dyin', Fowwest." Look, someone from Alabama doesn't do the whole "kill the wabbit" schtick.
A real southern accent can have many different effects. From some women, it's about the most erotic thing in the world. From some men, it makes you concerned for humanity's future. But one thing is for sure. Any authentic southern accent, no matter what the state, wasn't created at Warner Brothers.