Say the POD being Lee's trek up north going well and the US gets humiliated (though not broken). How would a vengeance-seeking US respond to free blacks and refugees fleeing up north?
In New England I can imagine blacks getting full rights, however in places like Missouri, Indiana or Nebraska...not so much.
Blacks in the US are going to be seen alongside the Republicans as the reason why the country broke in half, and are not going to be seen all that positively for awhile.
The US is still going to take to Westward Expansion and attempting to exterminate the Sioux and other plains indians, but since the Indian Territory ended up in the CSA, there may just be a larger flight of tribes like the Osage to the CSA.
In the CSA (if they have Kentucky), the Ohio River is going to be the target for runaway slaves.
Once slavery gradually disappears from the CSA over the next 50-60 years I suspect that a form of peonage and serfdom is going to replace the old slave system in the Confederacy. Some states being stricter than others. When it comes to political rights, blacks in the CSA are going to have very few, but, Jim Crow as we know it has been butterflied away. And with this *Segregation in the CSA, some states are going to be stricter than others. Because I can imagine that a Louisiana with a robust and important New Orleans is going to be much more liberal than Arkansas, Mississippi and parts of Tennessee.
If the CSA is able to get Arizona or any Mexican states like Sonora, Chihuahua and Sierra Leon (and nothing else), the Confederates are going to have to deal with the Apaches. I had a discussion about this with robertp6165 before he passed. The Texan one-time governor of Confederate Arizona, John Baylor, issued an extermination order of all the Apaches in the region, I can suspect that Texas is going to take this to heart, and include the Comanches in this extermination order. Other tribes in Arizona, for instance, the Pima and Papago tribes are going to be left alone, and possibly used as proxies against the Apaches.
The Indian Territory (Oklahoma) was mostly Confederate during the War and remained largely in CS hands until 2 months after Lee surrendered. And since this is an 1862-1863 victory, the only place the Union really holds is Tallequah, the Capitol of the Cherokee Nation at the time. The 5-Civilized Tribes, the Cherokee, Choctaw, Chickasaw, Seminole and Creek Nations all signed alliance treaties with the CSA and fought for the CSA in it's war of independence, alongside that, they were given representation in the Confederate Congress. Richmond is going to look very favorably upon that, the Indian Nations may most likely become an All-Indian Confederate state, Sequoyah will probably be it's name, so Turtledove got that right.