Time heals all wounds they say. But its amazing how long people can hold a grudge.
Following the Franco-Prussian War of 1870, the French made evening scores with Germany a kind of national obsession for 44 years. The Treaty of Versailles in 1918 had a big element of payback. And of course, things didn't warm up between the World Wars. I'd say add it all up, and you've got at least seventy or eighty years of the French despising the Germans.
Or look at the general loathing with which Japan is considered in Asia, a legacy of their War in Asia. They still occasionally have to apologize for that.
Finally, America as a country, is legendary for nursing a grudge. Don't believe it? Just look at Cuba. If there is such a thing as 'national character', then America's has many positive qualities. But a less positive quality is an amazing capacity for hatred and a willingness to hold onto that.
But as its pointed out, give things a century or more, and it all tends to settle down. People move on.
One thing that hasn't been discussed in this thread is Southern Society. The South was a vile and degenerate slave holding society, and slavery had come to be held in worldwide contempt and distaste. England had outlawed slavery in its colonies a generation before. There was a major abolitionist movement in the north. Given the South's commitment to this institution, I'm not sure how warmly the South would be received by anyone.
Even in our timeline, post-civil war, America's treatment of its blacks was a major open running sore that America was frequently criticised with. Any time America tried to publicly argue a moral stance, the issue came up.
South Africa and Rhodesia were international pariahs for generations. I can see the Confederacy being in the same boat. I don't think that the dissolution of slavery in favour of something like segregation and Jim Crow would have made a difference. And I don't think that, given the importance of cheap black labour to the South, that blacks were ever going to get a fair deal.
So, its problematic.