If anyone who considers the secession of the Southern States to have been been unconstitutional wants to be historically (and legally) accurate, maybe they should read the United States Constitution (as it then existed) instead...
South Carolina and the other rebellious states violated Article 1, Section 10 of the Constitution. There is no provision in that article (or anywhere else) for those restrictions to be waived if a group in a state say that their state "seceded". In fact there is no provision anywhere in the Constitution for any such secession to supercede the supreme law of the land.
We're conservatives, not liberals. We need to be strict constructionists and go by what the Constitution says, not by what it doesn't.
"..., that I do not consider the proceedings of Virginia in ’98-’99 as countenancing the doctrine that a state may at will secede from its Constitutional compact with the other States. A rightful secession requires the consent of the others, or an abuse of the compact, absolving the seceding party from the obligations imposed by it." - James Madison, 1832
I'm pretty sure that Madison read the Constitution, and the Constitution in 1832 was identical to the Constitution in 1860. So obviously people of the time both read the Constitution and believed the Southern acts of unilateral secession to be wrong.