You sometimes see reports on modern states' political polarization which claim that we must be very polarized now because fewer and fewer states have changed what party they voted for in presidential elections since 1960.
But LBJ's actions at the time pursuing civil rights flipped the Dixiecrat south to switch from Democrats to Republicans. Republicans which had been the progressive party of the North not 100 years earlier. It seems hardly surprising that these studies should "discover" that was a period of radical change in party affiliation starting in 1960 and stabilizing as time moved forward.
What I'm curious about is what party affiliation by state looked like prior to LBJ's presidential tenure. Was it more fluid, more changing, more evenly divided? With a few notable exceptions (the Bull Moose party and the Progressives come to mind), America was mostly still a two-party system for the previous hundred years, but I'm curious how the distribution of its voters changed over time.
The crux of this question is highly debatable. Fairly recent research by Byron Shafer and Richard Johnston in their book "The End of Southern Exceptionalism," (2006) argues that the party re-alignment in the South was not due as much to John's Civil Rights policies but instead to changing economic and demographic trends that changed the fundamental socio-economic makeup of the electorates in most southern states. In fact, they find that the southern working class whites continued to vote Democrat.