I don't believe it was anything like that. I don't think Duane was a liberal, but who knows? And "political correctness" was really not in vogue back in 1970. Plus, the Allmans were/are pretty proud of their Southern heritage.
I think Duane probably thought that "Little Dixie" might be considered insulting to the great land of Dixie.
Political Correctness was in vogue among hippies (if not the Allman Brothers). The MC5 tried to play up to their image as politically aware musicians (their manager was a radical) but they got called out by those really down with such movements.
New York punk (circa 1974) was in part a revolt against politically correct dogma (and noted as such in Leggs McNeil's oral history of punk rock "Please Kill Me" which has comments from many of the players in the origins).