Wouldn't a Bay of Pigs that's provided with heavy American air support, or an outright invasion by the Marines, be more likely to succeed? Granted, Cuba could be a serious hot zone of insurgent activity later, but I'd imagine that in the short term (at least Nixon's first term) the US would have no trouble toppling Castro and installing a pliant regime in his place. Probably not one led by Batista since he's already badly tainted, but I could see Nixon recalling
Carlos Prio to be Cuba's provisional president until new elections can be held, or something like that.
Agreed. I think Nixon would have a harder time passing civil rights legislation than JFK or LBJ did, simply because he's a Republican - the real-life LBJ pushing through the Civil Rights Acts of 1964 and '68 seems to have been, ironically, a domestic Democratic equivalent of 'only Nixon could go to Red China'. Without LBJ being the main pusher, I think Nixon will have a steeper hill to climb against a more steadfastly segregationist Democratic Party, although public opinion will be increasingly on his side as time goes on so it may not matter all that much in the long run. That ball's already started rolling with Brown v. Board of Education, Eisenhower's use of federal troops to enforce desegregationist court decisions, and the Civil Rights Act of 1960 after all.
The idea of a GOP that retains the black vote, having been the party of emancipation and now civil rights, without the Great Society (as I doubt Nixon or any Rockefeller Republican successor of his, no matter how liberal, would go to the lengths LBJ did in that regard) is one that I find intriguing - they'd have to work to retain and grow the black middle class instead to keep those voters on board economically. Perhaps we'd see the evolution of the Democrats into a socially conservative (in general - ex. on abortion, gay marriage, drugs, etc., not segregation or at least not exclusively) and economically populist party to survive after segregation becomes a settled issue, while the GOP comes to resemble a libertarian party writ large on both social and economic issues?
I think it might be the other way around if Nixon goes all-in on Cuba. If he's busy fighting Cuban insurgents, he might keep a lighter hand in Vietnam relative to the Kennedy and especially Johnson administrations, with US troops in the country never numbering more than a few thousand 'advisors'. Whether that'd be enough to keep SV afloat is certainly debatable though, especially if Nixon leaves Ngo Dinh Diem alive, which I've heard conflicting things about: on one hand Diem was quite corrupt and exacerbated domestic tensions with his efforts to impose Catholic primacy over the Buddhist majority, but on the other he was South Vietnam's only leader with genuine nationalist credentials (as someone who opposed French and Japanese rule) and when he was killed IOTL, Ho Chi Minh was quoted as having said something along the lines of 'I can scarcely believe the Americans would be so stupid'.
I can't imagine Nixon would lose reelection unless he really messes up, but I do think a Democratic victory in 1968 is highly likely. Then again, maybe not if support for segregation craters outside the Deep South and the Democrats tie themselves to that ship too tightly - and defeat here would provide that party with the impetus to finally attempt a realignment away from diehard segregationism. Perhaps a defeat for Lester Maddox or George Wallace in '68, then a still-Democratic Reagan defeating the Republican incumbent (perhaps George Romney, who was known to be dovish moderate and an early frontrunner in the real 1968 GOP primary) in 1972 on a more broadly conservative and less overtly sectional platform?
Fully agreed, that debate seems to have been one of the most prominent missteps of Nixon's 1960 campaign.