You seem confused:
1) During the Antebellum and post-Civil War periods, the Democratic Party represented the conservative south. The liberals were the abolitionists within the Republican Party, like Lincoln.
2) Between the Compromise of 1877 and the Civil Rights Marches, the issue of race was largely taken off the political table. During this period, in the very late nineteenth century, there was political disruptions among the two parties and people began to shift. For some 60 years, conservatives and liberals could be found in both Parties, working together and reaching across to get major projects accomplished. Hence, the two Parties being described as "big tents."
3) Circa the Civil Rights Marches, the Republican Party began to represent the conservatives, building upon a Christian-based platform, whereas liberals (hippies, war protestors, minorities) gravitated towards the Democratic Party.
Notice how the KKK, no matter which Party represents them, is always among the conservatives. The conservative South were the traders who seceded, rejected the American flag, created a Confederate war flag, and started the Civil War. The conservative South created the KKK and Jim Crow laws. Conservative Republicans voted against (or abstained from voting) the Civil Rights Act and the Voters Right Act. It's always Texan conservatives who threaten to secede during tantrums. Today, Conservative Republicans shed tears over their Confederate statues and ignorantly wave the Confederate war flag next to the American flag.
I mean, this line is simple to follow. This isn't hard. Throughout the American history, conservatives have always been a national impediment and always the source of treason. Even at the Presidential level, conservatives have Andrew Johnson, Richard Nixon, and now Donald Trump.