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Try a different analogy, namely the modernn EU and Brexit: (B = Brexit)

Was the leaving party a full member of the body politic
ACW yes, B yes

Did the leaving party enter willfully and freely into the government
ACW yes B yes

Did the leaving party have full representation in that government
ACW yes. B yes

Did the leaving party attempt to have their grievances redressed (Leaving our the beginning of hostilities here since it’s not applicable to Brexit)
ACW yes*. B yes

The leaving party left because of substantial disagreement with the government over what they believed to be a critical issue
ACW yes (slavery). B yes (immigration policy)

* I take issue with your judgement that the South did not try to have their grievances redressed before resorting to war. Most of the significant historical events of the first half of the 19th century dealt with the South trying to secure its interests through the political process and the compromises that were reached with the North that postponed hostilities. The war would have likely begun at least 40 years sooner had the South truly not attempted to have their grievances peacefully redressed.

I also am not addressing the legitimacy of the reason for secession in these two cases, only the legitimacy of the act of secession. The act of secession itself can be legitimate even if the reason for that secession is repugnant (as was the case for the Confederacy). There are those who might argue the same for Brexit as well, claiming it’s based on xenophobia and white supremacy. I reject that characterization, however. A sovereign state has the right to control it’s borders and immigration policies.