During the 1960 elections Nixon picks Thruston Ballard Morton as his Vice President instead of Henry Cabot Lodge, he was in his top three possible picks IOTL. This Nixon picks a Southern moderate rather than making a Faustian pact with the racists. Assume Nixon ekes out a victory as the Thruston VP pick pay dividends.
Thruston Ballard Morton was from Kentucky, but also pro-Civil Rights. So in 1960 and 64' the Nixon campaign focuses on the Southern Border States rather than the Deep/Solid South. There'd be no Southern Strategy, and Nixon would champion Civil Rights, albeit it would probably not be as strong as OTL Civil Rights Acts.
But in 1964 and 1968 a Dixiecrat splits the Democrats and allows the Republicans to win handily. The Republicans are seen as champions of Civil Rights, the Dems either have to make the Faustian pact with the Dixiecrats or keep having their votes split and never winning a general election. The new-found Black voter base will help the Republicans win in the Southern Border States and swing states for years to come.
Maybe after this have the Rockefeller Republican faction prevails while the Democrats are still fractured, earlier Nixon and later Rockefeller Republican faction victory at least butterflies away the far-right neocons.