There was a lot of tension between the Dixiecrats and the mainstream of the Democrat Party in the late 1940s. They walked out of the 1948 Democratic Party's National Convention and organized a third party. It is best known as the Dixiecrats today, but its official title was the States' Rights Democratic Party. Strom Thurmond was their presidential nominee and he won 39 electoral votes in the 1948 election, almost costing Harry Truman the election.

After 1948, the New Dealers and establishment members of the Democrat party scaled back their civil rights agenda in an attempt to mollify the Dixiecrats and prevent them from forming a more serious and long lasting third party. That changed after JFK and RFK began to show renewed interest in Civil Rights, after 1960.
Source:"1948: Harry Truman's Improbable Victory and the Year that Changed America" by David Pietrusza