You seem to be missing the point. Were you not paying attention? In 1965, the Democrats had two factions, the "Dixiecrats" and the rest of the Democrats. The Dixiecrats were pro-segregation and anti-civil rights, but they continued to vote Democratic for historical reasons. John Kennedy proposed the Civil Rights Act, and Lyndon Johnson continued pressing it after Kennedy was assassinated. The Dixiecrats opposed it, but the Democratic majority allied with the Republicans and passed it (that was back when bipartisan activity still happened in Congress).
After the non-southern Democrats and the Republicans passed the civil rights act, the Dixiecrats got fed up and stopped being the solid south. Over time, Nixon's "southern strategy" wooed them to the Republican party. The passage of the civil rights act was one, but not the only, reason the Dixiecrats left the Democratic party.
Here's a map of presidential voting in 1960: https://en.wikipedia.org/wiki/... It's pretty visible that except for Florida, the heart of the former confederacy was solidly Democratic.
The southern states essentially switched from Democratic to Republican parties between the early 1960s and the 2000s.