Red Necks acquired red necks by bending over in the sun while they built this country.
I heard it was that they wore red bandannas around their necks in some kind of labor dispute for identification — that the sun-burned necks had nothing to do with it. I suppose there are all kinds of stories.
That isn't the origin of the term. The first time it appeared in print was in connection with coal miners at the Blair Mountain mine in West Virginia when miners marching in support of collective bargaining all wore red bandanas as a sign of their solidarity.