Thurmond has his people vote for Truman after forcing him to drop or at least slow-walk civil rights. The CRA/VRA then happens under a Republican president and congress in the late 1950's.
Why? The Republicans were in charge in the 1950s as it was, and did pass the rather limited and ineffective Civil Rights Act of 1957 (which Thurmond infamously filibustered), but didn't go any farther than that. I don't know if Thurmond forcing Truman to back off on Civil Rights (which I'm not convinced he would do) would change much in the long run. No matter how much the Dixiecrats kicked and screamed and even delayed it, the party was moving forward on Civil Rights one way or another. If Kennedy still wins in 1960, nothing much changes probably.
