So long as three aren't mutually exclusive nothing I said is in error. White trash is clearly compatible with both, quoth the Wiki,
"In common usage "white trash" overlaps in meaning with cracker (regarding Georgia and Florida), hillbilly (regarding Appalachia), Okie (regarding Oklahoma origins), and redneck. The main difference is that "redneck," "cracker", "Okie", and "hillbilly" emphasize that a person is poor and uneducated and comes from the backwoods with little awareness of the modern world, while "white trash" emphasizes the person's moral failings."
Maybe you can finesse out an incapability between "redneck" and "hillbilly" based on the etymology-- the redneck can only be a Southern flat-land farmer while the hillbilly must be an Applachian hill dweller. But that' s just being nit-picky and pretendious, which is exactly what your post is.