The association with this terms of "Redneck" and "Billies" to illerterate and lower class peoples would have to have come from those who opposed William III's reforms and his followers. Those who backed James II and or where against the 1689 Act of Toleration, partially restoring civil rights to Roman Catholics and Dissenters. I believe some of the Anglicans of the Colonies would have fit some of these characteristics and would have gladly promoted making these identifications insults.
David