There are a lot of issues with the idea of a “National Divorce”. Legal, logistical, economic, military-related issues immediately spring to mind, but I’m going to focus on the socio-cultural ones instead:
1. The entire reason for this is because the losers of the culture war are desperate to claim some form of victory. Had they been the winners, they would not be entertaining the idea; if the losers in this alternate reality proposed it, they would have laughed in their faces and forbid it “for your own good”. While we don’t have to apply the same reasoning, as far as I can tell, the main reason why anyone who is not them is willing to semi-seriously entertain that in this reality is because we’re getting real tired of their shit, which is a short-term emotional reaction to a long-term issue. If it’s going to be allowed, there needs to be a much better reason than either side has given thus far.
2. This is admittedly intuition on my part, but I would strongly suspect that during and after the transition period there would be a stark difference in how the states handle population migration/swapping. The more liberal states would probably make at least some effort to help people move in and out of the state to help ensure that people get somewhere more politically and/or culturally suitable to their needs, but given all the other issues which will be straining the system during the transition period, some might make only an insufficient or even token effort in that area… and probably not bother to change much after.
Meanwhile the more conservative states are going to forcefully eject some of the people they consider “undesirables” and confiscate anything of value, and/or refuse to let certain people leave so they can have some designated third-class citizens to abuse. I suspect that the specifics would vary greatly by state; for example, I would expect Idaho, which is almost entirely white, to try to purge itself of non-whites, while Mississippi, which is like 40% black, to try to keep as many black people as possible and institute some form of “don’t call it slavery, but for most practical purposes, it’s slavery”.
3. Florida and Texas. Florida is a centrist state by demographics but the Republican party has had a stranglehold on politics for a few decades now, due mainly to severe vote suppression and oft-suspected elections fraud (which the courts are reluctant to look into); Texas is a moderately conservative state which is in the process of a demographics shift which is expected to result in a moderately liberal state by the early 2030s, and their Republican party is eyeing Florida for ideas. Assuming that they fight to keep near-absolute conservative control over those states in a national divorce, that’s going to be an ugly and likely catastrophic mess, given how many liberals and centrists are going to be like “no, it’s not *just* your state, and without federal rights and protections, we’ve much less reason to put up with your nonsense”.
Probably missing a few things, but those are the first which came to mind.