The article mentions "It turns out you don’t want to sound southern, either. Although pretty imprecisely estimated, it is almost as bad for your wages to sound southern as it is to sound black, even controlling for whether you live in the south."
There are many southerners who speak with a rather sophisticated gentility, then there are those who speak with a quaint but kind country accent (many farmers). Or just those southerners who use southern words, such as "y'all" and "coke" (as a catch-all term for soda).
The redneck accent I speak of his found in rural places, not just in the south. Often condescendingly referred to as "trailer trash" or "white trash". But I suppose that the distinction is pretty arbitrary and not very well defined.
The problem of many speakers of southern dialects of English in much of the United States is that speakers of broadcast varieties of General American English tend to lump all "southern accents" in a category that includes the redneck accents and the plantation-owner-descendant accents without further distinction. And that is why, as the article reports, there is an employment opportunity disadvantage (on average, other things being equal) to sounding like any kind of southerner.
(I have been to all fifty states, having traveled to many states as a Chinese-English interpreter on contract for International Visitors Program of the United States Department of State. I can remember one case of a very upper-crust Mississipian, who was then living in Alabama, having an English accent that to my Midwestern ear was quite nonstandard, even though I was aware that in the south it would be taken to be the accent of an educated person from prosperous family.)
So for better or worse, I have neutral American English.
Pretty good being on top.
I think that the most non-standard redneck accents I have heard are those in Vermont. It's a strange mix of hippie and redneck.
And then there are southerners who use "soda" as a catch-all term for pop :)