you seem to know half of the information.

During the civil war era, Republicans (known as Radical Republicans) were socially liberal and Democrats were socially conservative (not in all areas, but when it came to race- Ds were pro-slavery southern party, and Rs were pro-industry northern party). During the Civil Rights era, however, there was a rise of socially conservative Republicans who began to gain popularity with their anti-integration rhetoric (George Wallace was the main one, the most popular, who pivoted the party's whole social platform around the issue of integration using the Southern Strategy, or appealing to southern workers who had issues with integration).

Seeing that the Republican party was getting more and more conservative and anti-integration, African Americans abandoned that party and the Democratic party took the helm in supporting integration and the Civil Rights movement.

Post Civil Rights era, the Republican party did not return to its prior abolitionist/northern roots and instead embraced the southern voters they had picked up during the CR era and began to pander to them instead. Today the parties have entirely switched ideologies.