The Southern position in 1861 was the right to unilaterally secede from the Union to protect their institution of slavery from what they saw was the threat from a Republican administration.
So, you placing a label on Southern people of 150 years ago with that simplistic narrow generalization is a misrepresentation of commonly known facts.
Fair enough. Name one Republican who supported the Southern rebellion in 1861.
The 'states rights' position of non-seceding states was most important in view of the several Northern states engaging in nullification of laws designed to protect what was then widely accepted as humans as property.
Their disagreement would have been with the federal government. And that government, as well as the court system, upheld their rights in every instance. At the expense of the state's rights of the Northern states.
The Federal government had specified the right of Dred Scott to be held as a slave. The nullification states continued their open disregard of the law.
Any attempts at nullification had been struck down every time they reached the Supreme Court. Again, the federal government lived up to its obligations to the Southern states in every regard.
The final straw, or the partial list of causes of the secession were the reapportionment of the Congress, the dominance of one party,and the expansionist and tariff raising planks.
Please point out to me where any of those were prohibited by the Constitution. The South had, and continued to have, a disproportionately large representation in Congress, but they were not guaranteed equal footing with the non-slave states. Nor were they guaranteed that the Democrats would remain the dominant party. And tariffs were not illegal.
Secondly, the secession was due to the numerous violations of the Constitution.
The Constitution is not violated merely because the Southern states said they were.