There is a reason liberal demoncrat are called racist... Because they always have been, it is the heritage of the demoncrat party since its beginning, history proves that out.
First, you're wrongly conflating "liberal" with "democrat", here. Racist democrats were never "liberal" democrats except in the minds of modern "neo-cons" intending to slander anyone who doesn't agree with themselves.
Secondly, what you're referring to is the fact that southern racists were originally mostly democrats, because they were mostly poor and middle class, and the democratic party was the party of the poor and middle class. That changed in the late 1960s when two democratic presidents (Kennedy and Johnson) backed the equal rights for blacks. When that happened the racist democrats in the south, and some in the north, turned their affiliation to the republican party, because the republican party was willing to pander to their racism.
And those voting blocks are still republican to this day, because the republican party is still pandering to their racism, their religious bigotry, and their general xenophobic attitude toward anyone not like themselves.
None of which has anything to do with liberalism or conservatism. Only politics and xenophobia.