And contrary to the OP, these results don't demonstrate a reversal of the predictors (i.e., that actually being a Democrat predicts voting for the Civil Rights

And contrary to the OP, these results don't demonstrate a reversal of the predictors (i.e., that actually being a Democrat predicts voting for the Civil Rights Act and vice versa), but rather than we're possibly using the wrong predictors. That is, rather than demonstrating that there is a different correlation between party and vote, it demonstrates that there is a (stronger) correlation between geography and vote.