How would Civil Rights go under Nixon? Ironically, I'd call LBJ's handling of the issue in the 1960s very much a "Nixon goes to China" scenario. LBJ was very Southern, very Democrat and very well connected. Nixon isn't Southern, isn't a Democrat and is forever defined by his lack of beltway panache. Also unless he oversees a parliamentary revolution, he's dealing with a Democratic Congress. So do Nixon and LBJ cut a devil's bargain to get a CRA passed ITTL?
How do dieherd Dixiecrats react to Nixon if he starts ordering troops to enforce desegregation? How do the Democrats as a party react to Nixon leading the charge? Do we see a Democratic civil war? Without having the POTUS and LBJ behind CRA and instead Tricky Dick, how many blue congressmen who supported out of tribal loyalty IOTL don't for Nixon. And how many basically pro-CRA congressmen decide they hate Nixon more if the Democrats as a whole are seriously divided?
Do we end up with the Democrats suffering a lost decade in the 1960s as their Dixiecrat elements try actively fighting segregation, alienating the general public, while a lot of liberals jump to the GOP (including the future neocons early ironically). By the time they get their act together in the mid 1970s, they're aiming for centre but they've lost a lot of middle-class liberals, as well as black voters in general, the South 'blue dogs' having a lot of sway. Do they end up the Blue-Collar White Guy Party? Representing New Jersey sewage workers just as well as the Georgia farmer or Chicago cop. Not so much Red Tory as Blue Labour but of a very vague, safe centrist patriotic flavour. With a trucker hat somewhere. And an Eagle.
The Republicans might well lead the monetarist charge, perhaps "Hollywood Liberal" Reagan institutes his own version of rigeur? Reaganite Neoliberalism. If Nixon gets positive results in Cuba and Vietnam, the ideas that fuelled OTL's neocon hawks ITTL could end up the touchstones of Nixonian Liberal Interventionism.
Who gets control of Cuba when Castro gets taken out? Does Batista return or is he too much of a joke after he fled the previous year? Another strongman? How do Cuban-American relations develop? Despite very different circumstances I imagine the emigre community will still be large for economic reasons, depending on Cuba's prosperity and stability.
No Communist Cuba kills a lot of butterflies. For one the Marxist guerillas of Latin America and Africa are a lot less well supported.