The Confederate states just traded Washington telling them what they could do for Montgomery telling them what they could do.
Yes and no. State's rights, at its most basic level, has to do with political self-determination, not any temporary issue like slavery. The Confederate States joined the CSA knowing what the Confederate constitution stipulated - the State's rights aspect of it comes in with their right to make that choice of association, not the subsequent restrains which they acceded to.
All the same, it is ironic that given everything else, the South's interest in slavery would actually have been MORE protected by remaining in the Union than by leaving it, once all the factors are weighed.
From a Texas point of view, this either/or debate is rather curious. We didn't agree on why we seceded and why we fought.
Many of the boys called to fight believed it was a war waged on behalf of the slaveowners, but they fought for the right of Texas to decide the issue.
A goodly number of the Germans wanted no part of it and sent their young men to Mexico to sit it out.