As a matter of amateur sociolinguistics, I actually do think Schweitzer is correct that many southern men talk in a way that comes across as stereotypically gay to those of us used to the more reserved mannerisms of regions like the upper Midwest (or Canada, in my case).
I've noticed that too, when traveling in the Deep South. It seems particularly common in Alabama for some reason. There's a tendency in Southern speech towards a somewhat nasal tone of voice and to vocalizing from the mouth rather than from lower in the throat, if that makes sense (not sure what the technical linguistic term is); those are features that also occur with the "gay voice."
There's also a weird bipolarity in Southern notions of masculinity - it's simultaneously this rugged alpha-male who drives a big truck and works a blue collar job and is rough around the edges, and the archetypal dandy "Southern Gentleman" who is neat and well-dressed and genteel in demeanor.