Why imagine? We experienced this in the 1860s. Unfortunately our reaction was not to veer hard in the opposite direction, and much of the rebels’ ideology persists in our government to this day.
For starters, the south didn't overthrow anyone's government; they opted to leave the Federal union.
Secondly, there was no appetite for continuing the war longer than 1865, or for extending Reconstruction much past Grant's term of office. A prolonged occupation of the south, such that white people there could be taught that white-supermacy-is-wrong-m'kay at gunpoint until they finally understood...that doesn't happen in this timeline or any proximate one.
I'd like to understand your comment better but I really have a hard time understanding what happened in the USA in the 1860s. Just like TangoTrotFox was kind enough to assume that not everybody here knows Bavarian history by heart, can you not assume everybody here is American?
I googled for "USA 1860s" and followed some links but I can't get further than stuff like the "Dakota War of 1862" which I doubt is what you're referring to.