Uhh...
The Republicans, liberal and otherwise, are the ones that promoted and passed civil rights laws in the 1960s.
On the other hand, while Southern Democrats were almost solidly against civil rights legislation, Northern and Western Democrats supported it, as did Presidents Kennedy and Johnson. In the early 1900s, as blacks left the South in large numbers for Northern urban areas, the Democratic political machines cultivated their votes. These urban centers had large numbers of immigrants from different European nations, and the Democratic politicians set up political clubs in ethnic neighborhoods. Blacks were just another ethnic group to be won over with patronage. While blacks, when they could vote in the South, supported the GOP, they increasingly supported the Democrats in the North.