I grew up on the Uncle Remus stories too, and also my beloved Pogo, and both were indispensable influences on my childhood. What Churchy La Femme calls Southern Fried Speech has been part of my speech center for 60 years.
Sorry if this offends, but by now it is part of the way I talk. You'll find me inescapably on the side of dialect, if only because my infant ear was imitative and alert for ways people spoke, so I picked it up before I knew better. I couldn't help it; my ear wrestled my voice flat on the mat, and I'm one of the many people who suffer from this.
I've had to do my best not to sound like I'm parodying the people I'm with. My head is an echo. It's a flaw I guess but I can't overcome it. I speak in many voices, and they're the voices of people I've loved or who have been influential on me, including blacks. Not that I could necessarily reproduce them accurately or even come close! But they have tinged my talking and singing.
And all my life I have needed to hear the dialect in stories and songs I've loved when heard that way.
So, in my inept way, I've found myself "sounding like" different regional accents, Scots, Irish, Southern white, Southern black, cowboy, and so on because to me, the sound is built into the song. When I hear someone denature a song by singing it in straight middleclass English, I am grieved and feel half its soul has been taken away.
I too am sorry for, and understand, those to whom dialect, particularly black dialect, is a lingering trace of Jim Crow or other forms of discrimination. All I can say is, I think they are taking the shadow for the substance.
Real discrimination is not in the voice, not even in the blackface stage. Real discrimination is in belittling, cheating, manipulating, and stunting the lives of target populations. So go look for your tormentors among the politicians, rentiers, commercial interests, vote suppressors, and others who live by racism but never seem to get the blame they so richly deserve.
Irishmen, who are among my ancestors, have luckily gotten over their shame and anger at mock-Irish speech. The day will come when blacks feel secure enough to do the same.
Meanwhile, it's an uncomfortable fit. I try not to insult anyone if I can help it. But sound IS music and inseparable from songs. Can't stand to sing 'em any other way.
And, of course, if I have to avoid singing a certain song in a certain situation because it will be taken as prejudicial, I try to do that, and be sensitive to who's listening, including people who may form a prejudicial opinion, like children and bigots.