...just a gut feeling that, as you described him, a "stereotypical ultra-Yankee" wouldn't have even come close in the south without the support of that bloc. Voting or not, they could still organize with and support his campaign; and this might be somewhat myopic, but I imagine such an oppressed and disenfranchised group would be more inclined to stick their necks out for the young, inspiring Irish Catholic from the north than they would be for Johnson (as a matter of optics, regardless of their actual records). However, I also think Johnson would have done better in the south, for that same reason. Fewer African Americans supporting his campaign, less talk of civil rights perhaps, and broader appeal to "traditional" southern Democrats would likely give him the edge over Nixon in the south, widening his margins compared to Kennedy's IOTL. It may have been common knowledge that LBJ was a supporter of civil rights legislation well before he became President, but it was also well known on Capitol Hill that he was a racist (or, at the very least, liked to drop the n-bomb frequently and even referred to the Civil Rights Act of 1957 as "the nigger bill"). The north is a different story, but I still imagine that Kennedy (again, as a matter of optics) had a better chance with African Americans there than did Johnson. Which is precisely why I say that, on the whole, LBJ does worse and ultimately loses to Nixon, which it seems like we agree on.
It seems to me that you are projecting the modern, post-civil rights situation, in which black votes matter because they do vote, and perhaps a segment of the "white" liberal/progressive voters (people like me) are influenced by getting the impression that African-Americans like a certain candidate. Surely such ultra-liberal "whites"* existed in some numbers, but small ones indeed, in 1960, and fewer still in the South, and these would be people of such political engagement that they would judge for themselves. Also being projected is the Saint John image of JFK that he acquired by virtue of assassination.
In fact, I think you've got the relationships with African-American communities backwards. Yes, indeed, as a Southern man of his generation, Johnson used certain words very freely and naturally, and I'm sure it had some sting for African-Americans hearing it...but Harry Truman was the same way. And Truman had done a lot for them, such as ordering the US military integrated. Truman did this because he was outraged by reports of gross injustice perpetuated on African-Americans and emphasized with them as human beings and fellow citizens, and while I've studied LBJ's personal motives less, I imagine it was much the same for him. Did either one see past the "mind-forged manacles" (not a scare quote that, that's from William Blake) fully, to truly recognize completely equal fellow humans and citizens as worthy as himself? Would they not be upset if his daughter were to marry an African-American? (A very rhetorical question in states like Missouri or Texas...it being plainly illegal in either, along with the majority of other US states until Virginia v Loving led to anti-miscegenation laws being struck down throughout the nation in the late 60s--thanks in part to some encouragement of the Loving family by Johnson's administration!)
I'm not pushing simple relativism here. Racism is poisonous and wrong, but you should recognize how deeply pervasive it was in the USA (and horribly, remains so, including among people who happen not to recognize it, and still others who, being called on it, still refuse to see that they are in fact being racist in their reactions; lots of racists swear to high heaven they are not and never have been). A Southern "white" person of the era would probably have the perverse virtue of not doubting that they have been and still were being racist, and either assert 1) it is natural by instinct and all or most "white" people would be whether they admit it or not or 2) it is a product of social training but a necessary and functional one (see Atticus Finch's speech in defense of an accused African-American client in
To Kill a Mockingbird for this reasoning), or, if very progressive, 3) it is a deep habit they were raised in, and reinforced by the normal behavior of every other "white" and for that matter African person around them, that they have come to know is not good, but quite heavy, and to go around trying to reverse it deliberately would destroy their ties to their home community.
I'm pretty sure Truman and Johnson were somewhere between 2 and 3, and perhaps had some reservations about just how far equalization of status of "black" and "white" should go, or if they were so insightful as to hope for total integration someday--which in the 1960s Martin Luther King had to describe as a "dream"--they understood, perhaps better than a Northern "white" who was raised to believe themselves free of racial prejudice, how much turmoil and difficulty would be involved, but perhaps also that what might look impossible to a Northerner, "white" or "black," who did not deeply understand Southern society, that indeed such change could come. Because a Southern "white" person who saw through the propaganda of race and recognized, even if only partially, a fellow human being beyond the race veil, would understand very deeply how constructed and artificial the so-called divide really was.
But one mistake they would never make is to suppose themselves free of all prejudices! They'd know they had them, trained reflexes to perceive things a certain way, and that it would take work to see past them.
So--one cannot judge that a person would automatically be more obnoxious to the African American community just because they used some nasty words associated with maintaining racism casually. African Americans, like oppressed people generally, would be observant of nuances. If the person involved is obviously Southern "white," but in fact does things for them that really matter, and makes efforts to be civil and friendly in person, then I think they'd want to know details of just how they use the "n-word" in context before judging whether they are dealing with a two-faced snake or a true ally and friend. I don't know for sure exactly how enthusiastic various African-Americans were about either Truman or Johnson but I think when the chips were down they supported both as much as they could, because deeds matter a lot more than words.
So relativism applies, in context, and appropriately enough, not in an absolute way. Truman and Johnson's example don't give modern "white" people license to follow their bad example; even a modern person who shares their excuses, being raised and immersed in a society that persists in racist imagery and a combination of sustaining old stratifications and complaining bitterly about them not being upheld enough, still knows that civilized standards require them to go farther, in either hoped for sincere reevaluation or at least a feigned civility, today. In 1960 this revolution in civil standards had not yet taken place and for politicians like Truman or Johnson to get too far ahead of the curve would have actually weakened their effectiveness in getting positive and useful, important things done on behalf of the African American community. (This does not bless them, exactly, but it does say that while the more gratifyingly true evolved Southerner friend of the AA community may have been the more alienated person who finally gets how nasty the n-word is, the one who has the traction to get concrete stuff done for them is the one who goes on sounding more conventionally Southern "white.")
And so, I think you probably have the images of Johnson versus Kennedy backwards in the minds of pre-1960 Southern African Americans. Looking at the latter, they see yet another Northern "white" man who doesn't particularly care about their situation one way or the other. He has some pretty words about better integration, but that had become boilerplate campaign rhetoric (outside the South!) since 1940 or so; the Republicans could always claim it, and it became expedient, despite the fears and protests of powerful white supremacist interests, not quite all of them Southern either, for Democrats to counter. And some of those Democrats who adopted the banner of civil rights were deeply sincere, and some of the most rock-solid of the sincere were Southern "whites" like Truman or Johnson. Who could look into Kennedy's heart? Had Kennedy in fact done anything remarkable on behalf of African-Americans in his entire political career, or was he just meeting his obligations to the Northern African-American voters and the fringe of strongly pro-Civil Rights "whites"? Being in a sense an outsider as Catholic would not be perceived as a positive by Southern "blacks" either.
But when they looked at Johnson, they would see and hear a man of a culture closer to the one they had to deal with every day, someone easier for them to evaluate. And he was someone who most definitely had done good work for them.
It is also very odd that you seem to think that AA people campaigning for a candidate would tend to help their victory numbers outside of AA (and perhaps other excluded ethnic) community circles. In fact you seem to acknowledge that visible AA support for a candidate would cost that candidate some significant numbers of votes in the South!
Some of your perceptions might actually apply to Northern African Americans, perhaps. I doubt it; the cultural ties between the two sets of AA people were still very strong, most Northern "blacks" being recent migrants with family ties back to the old Southern districts they were from and certainly deep memories. The urban experience, and the different legal environment, certainly changed perspectives. One apparent "paradox" to a "white" person studying 1960s history is stated along lines of "gee, in the 1960s African Americans gained tremendously relative to their former situation, yet AA communities became known for more violence than ever the more progress was made? What's up with that?" A lot of sage muttering about "revolution of rising expectations" follows, and nowadays perhaps the darker muttering of the beyond-the-pale crowd of pale folks who say "damn it, equality is a sham and what would you expect giving fake "rights" to inferior people who don't deserve it, nothing but trouble follows, we tried to warn everyone" is more heard than before, God help us. But open your eyes to a plain fact--the majority of Civil Rights era reforms were targeted against and effective against the sort of discrimination that existed in the South--specifically, legally enforced, blatantly and openly racist policy, was struck down by law. The state could no longer discriminate in voting, in permitting marriages, in education, and so forth. This did result in tremendous and immediate benefits for the AA population still living in the South, along with eliminating a lot of nasty local regulations scattered in the North as well.
But the form of discrimination taken most often in the North did not rely on legal reinforcement. It could and did take advantage of legal help when it could get it, but in many a state, overt and frank legal discrimination was disrespectable enough that laws would not be passed to enforce segregation. No matter though...white supremacy had and has ways and means of being enforced without the help of law, and even in the face of a zealous moral crusade against it with the law seeking to defuse and dissolve it. Critical masses of "whites" believing themselves entitled to being free of offensive AA presence and influence have ways of letting the latter know they are unwelcome no matter what the law says; customary differential reactions most people don't even notice are being deployed steer "whites" into and people of color out of privileged positions. It is illegal for educators, counselors, bankers, employers, government officials of any kind including police, and so on to advise or support or oppose a person differently based on the color of their skin, but of course not everyone respects that rule and they seek to subvert it consciously--but the most pervasive factor at work is the unconscious, unexamined reflexive reaction. The majority of the "white" people in situational authority who route people's lives to rise or fall in society would honestly swear race was not the determining factor, but the statistics show that it must be.
For these reasons, the Northern model of discrimination is quite different than the overt and blatant old Southern model. The latter being criminalized, the evolved coded way of thinking--most subtly forged mental manacles indeed!--has spread. In 1960 when Jim Crow was under challenge but still standing strong, Northern African Americans might or might not have reacted differently than their Southern counterparts, facing a different form of challenge. I believe that there too, Lyndon Johnson would have on the whole appeared as more their friend than John Kennedy, but I might be mistaken. Northern AA communities would include a lot of people born there who had not had the customs of how to survive encounters with Southern "whites" hammered into them from earliest childhood and would quite naturally resent the airs of such beings who would presume to judge them unto death on the "violation" of most irrationally varying "customs" and laws. Perhaps in the North even migrants who quite well remembered how to placate Southern "whites" would seize the freedom not to have to with glee. Dealing instead with the more insidious Northern form of white supremacy they might rather deal with a Kennedy--or a Nixon!--assuming a foe lies behind the smiling facade. They might discount all the solid work men like Truman and Johnson did as limited tokenism that does nothing to address the fundamental conflict, and figure that in the end, the African American has no "white" friends anyway, and it all relates to power.
But I don't think JFK enjoyed any strong advantage over Johnson in any non-"white" sector.
And in 1960 more than today, only the "white" vote, North or South, really mattered anyway. In such a marginal race as it turned out to be in 1960, every marginal bit turned out to count, and there probably switching African-American votes from Democratic to Republican would have thrown the race to Nixon. But neither candidate would have campaigned with that sector largely in mind! Nor would LBJ.
I think LBJ would lose among "white" voters, and while I can't be sure I think he'd consistently be more respected among non-"white" voters...but these would only in some places be significant, and in those places even very strong support for Johnson would be more than countered by weakening it among "whites."
Again I also say we should avoid looking at Kennedy through modern eyes, because of the rosy filter of sainthood he had bestowed on him by assassination which dazzles and confuses us. We know his Moon Race initiative paid off in a successful moon landing and a bunch more to follow (and one disaster which the crew survived); we know that he came out of the Cuban Missile Crisis having not blown up the world; we know that the successes of the Civil Rights movement, such as they were, reflect glory back on Camelot in general perception. The latter at least is Johnson largely sacrificing himself to make the reforms effective--by retrospectively calling on the blessing of the Sainted Kennedy, he helped overawe heavy skepticism. But in fact it was much more Lyndon's work than John's. But giving Kennedy the credit had the effect of nailing it down, so Johnson promoted Kennedy's image as a civil rights warrior posthumously.
I think the view of Kennedy at the time was a lot less colored and blurred! Still he clearly had a glamor that Johnson lacked. The point here is, we should try to see JFK as he appeared before he was shot rather than project on prior voters some sort of premonition of Kennedy's iconic importance in the future.
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* I make it a policy to avoid color terms for people, and if I lapse into doing it to always put "white" in scare quotes because I believe it to be a false category in an essential sense; people mistaking it for an essential, fundamental, natural category perpetuates very much mental mischief, and the categories exist socially speaking for quite nasty reasons that among other things confuse people.