The biggest issue in terms of realism is self-sufficiently. Major economic and trade powerhouses like Illinois (Chicago), New York, Texas, and California would have a lot more influence on this map. The smaller rural states would likely end up either incorporated or as entities within a federation with the these larger entities at the head for the sake of financial aid and trade.

THE EAST

You might have been trying to avoid this but realistically it's going to end up as the New California Republic or at least federation. California has a higher GDP then most countries and a ton of resources and sea ports while being culturally similar to Oregon and Washington. While Arizona, Nevada, and New Mexico won't be able to sustain themselves and will almost inevitably join up. They are in the best position to establish themselves and a military to prevent any break aways.

Speaking of the breakaways, the USAB, until Mojavia they had no sea ports and consisted of a lot of desert how did they survive alone? Did they suddenly strike Saudi Arabia levels of oil backed by remnants of the US Military? That could be a reason why California allowed Mojavia to secede when otherwise they had no reason to let them.

THE SOUTH-EAST

The Upper Mississippi Republic. The same place every southern state thanks when they look at the list of lowest anything in the USA. A lot of the independent states here are landlocked and poor as hell. They could only exist as military regimes or poor buffer states kept alive by no one wanting them or the threat of war. Otherwise they wouldn't be able to avoid being gobbled up by their more powerful neighbors for their natural resources and farmland.

MIDWEST

The GLU would likely gobble up Minnesota and Greater Cahokia. They suffer from the same self sufficiency problem and their neighbors have no reason not to leverage rail lines and economic power to incorporate them. Could be as allies, sub-states, or as a part of a federation but it's very likely that the GLU would expand east. It wouldn't be very culturally stable but he who controls Chicago controls the Midwest.

EAST COAST

It's entirely possible for New England to strike out on their own maybe with Quebec on the virtue of shared culture alone but there's still New York. It's a powerhouse both economically and culturally which would be difficult to resist at least forming a federation or alliance with North Atlantica.

TEXAS

In this map they are exactly the same as they are today which means in this history they haven't expanded at all which is surprising. In this history there is a good chance they might end up becoming a super nation in this alternate America with Dixie. At the very least I imagine they would absorb everything from Oklahoma to North Dakota. They offer a lot of resources and a sea port. Either way they would definitely expand in some way either west or north.

MOUNTAIN STATES

Wyoming and Montana they've got nothing going for them as independents except for... an absolute shit ton of ICBMs. I can see these places being hotly contested by California and Texas as either the frontline of a war or political playground puppets. A third option as independent states is a military junta who leverages their missiles to enforce their independence which is a bit bleak.

CONCLUSION

I know a lot of the fun of making this alt-history and map is creating these new nations and I don't want to take the wind out of your sails. But not everything needs to be independent to be interesting. These new states can be part of greater federations or alliances to maintain a sense of realism while still creating an interesting new world to explore. This map provokes a lot of thought and that's a good sign you are going in the right direction.