After World War II, during the civil rights movement, Democrats in the South initially still voted loyally with their party. The signing of the Civil Rights Act of 1964, however, was the last straw for many Southern Democrats, who began voting against Democratic incumbents for GOP candidates. The Republicans carried many Southern states for the first time since before the Great Depression.
When Richard Nixon courted voters with his Southern Strategy, many Democrats became Republicans and the South became fertile ground for the GOP, which conversely was becoming more conservative as the Democrats were becoming more liberal. However, Democratic incumbents still held sway over voters in many states, especially those of the Deep South. In fact, until the 1980s, Democrats still had much control over Southern politics.
It wasn't until the 1990s that Democratic control collapsed, starting with the elections of 1994, in which Republicans gained control of both houses of Congress, through the rest of the decade. Southern Democrats of today who vote the Democratic ticket are mostly urban liberals. Rural residents tend to vote the Republican ticket, although there are a sizable number of conservative Democrats.