Here's the cultural piece here though: you have the African-American experience in the USA as much more of the standard immigrant experience. They came from elsewhere fleeing the awful; this contrasts to the OTL experience of being a continual reminder of the USA's original sin. An and original sin that the white population will often be finding ways to subliminally justify to themselves up to this day. Without the South in the US, I would predict that a lot of the structural racism that post-dates Appomattix (the standard chain email stuff) isn't as needed to square the traditional story of America with the reality. They become a community whose story starts when they ran North.
I mostly agree, though, TBH, structural racism was ever "needed" to "square" anything. More than anything, actually, it was used as a tool to divide and conquer, just as in the South, even if more covert up North.
Secondly, I think you'd have a weirder sort of CSA sympathy in Northern culture. Now before anyone says "how could any US citizen like or idealize the country their forefather fought and died to stop" - look at this board. Or look at post-1900. The glamourous gray uniforms can make people smolder across time...
It might happen in certain circles, that is indeed possible; mainly with more hardline social conservatives who might greatly resent all these "coloreds" coming up North and "adulterating", what they see as "white culture"(just as many hardcore racists do in the present era IOTL).
More practically, as I occasionally touch on, the OTL late 19th had a love affair with the concept or idea of eugenics that is hard to remember in a post-1945 OTL. Give everyone a few decades of reading their Austin Chamberlain, and the South will be far less apologetic about their (now viewed as farsighted) Cornerstone.
Yes, that's true for OTL, but was the height of popularity and scientific acceptance of eugenics that had eventually been reached just before World War I inevitable? I'm not so sure it was.
This will make the South look kind of cool in the circles those ideas are zeoulously believed, and the US and Europe OTL had plenty of those circles.
And, btw, this seems to assume that there isn't a significant backlash against eugenics based on the horrors that would be likely to occur in the C.S. starting towards the end of the 19th Century, which also seems unlikely, especially not if the actively anti-racialist branch of the Progressives(which were fairly noticeable even IOTL, but are likely to be rather more prominent ITTL) and abolitionists would have anything to say about it.
Take the proponents of American Empire OTL. Now give them a case where the smaller, weaker, and still ocassionaly despised CSA are being paragons of late 19th century "civilizing the lessor" to everyone who thinks as they do.
And it's not likely that many in Europe would be terribly accepting of how the C.S.A. does things; I can see maybe a more Prussian-dominated Germany, or even a more conservative Austria-Hungary turning a blind eye to all but the worst of the C.S.A.'s excesses, even if to mainly just put a stick in the eyes of the Brits and the French, but not much beyond that.
I almost wonder whether the US gets imperial earlier - or does even nastier things on the reservations than OTL.
Neither of these are terribly likely, especially not if the C.S.A. acts in a particularly nasty manner(such as towards Nicaragua or Cuba, for example).
Softer culture? I think you see a larger peace time military, a move to more short term enlistment around a cadre, and some state role in making damn sure there's plenty of rail capacity heading South. Those will have some knock on effects in the culture. As far as what the US is, there's a huge example of what the US is not that isn't there OTL.
It'd probably be a mixed bag: there might indeed be more veneration of the military(even if mainly because the Union was fighting the pawns of the slavers), but race relations are definitely likely to be softer on the whole(with a possible exception of a backlash by some of the more reactionary elements of society), even if some of that could be motivated by hatred of the C.S.A. than anything.
(Lastly, to head off something taking this off track, I'm positing a realistic CSA victory scenario. Thus, there is no Confederate Kentucky, Missouri, or Kansas. A surviving Albert Sydney Jonston does not capture Chicago. The state on the ground in the west during any likely peace date means that the Mississippi river is either open - I think you can make a case for big chunks of territory down the river staying US. West Virginia might keep digging coal for the North that usees it. There's no aw shucks, just take the South west so you can have a Pacific Coast either. This is a CSA that could have been, not one that allows the CSA to sweep in at the last minute to blow up the whole IJN.)
I dunno what this has to do with the Imperial Japanese Navy, but it's not *entirely* impossible that the C.S.A. might indeed be able to snag Sonora + Chihuahua under certain circumstances: Mexico could suffer a civil war similar to OTL's at some point, and if a guy like Porfirio Diaz is in charge, he might just be willing to make a deal with the Confederate "devil", as it were, and hand over those two rebellious states to the C.S.A.(remember, both Sonora and Chihuahua were both major centers for the revolutionaries during OTL's incident). At least with Diaz, I wouldn't put it past him.