As I say, the reconciliation was real and broad, but it wasn't entirely inclusive. African-Americans -- especially in the South -- were mostly left out of it. The soldiers on both sides of the Civil War had been mostly white, and this turned out to be a reconciliation between white Northerners and white Southerners. Segregation in the South and discrimination in the North continued.
This is not to say that the reconciliation between the North and South was not important, only to say that it was incomplete. We still await the reconciliation between Black and White. Whether we will get there by the means currently employed by those shouting the loudest right now is an open question.
But I remain hopeful. If you go to the Little Bighorn battle site on the Crow Reservation in Montana, you will see a Peace Monument there. The Sioux and the US Army finally reconciled their differences and made peace. But they were not alone: this is a monument to a three-way peace. For the three peace-makers were the Sioux, the US Army, and the Crow. The hostility between Sioux and Crow is an ethnic conflict of long standing. The Crow aided the US Army against the Sioux. But the Sioux and the Crow have now made peace, too.
Someday, I hope to see monuments to racial reconciliation. To do that, ordinary people of all backgrounds have to engage each other. We have to build a world of shared values and shared heroes. Letting the most bitter and most rigid try to impose their version of reconciliation upon us only prolongs the agony.