Thomas Jefferson sure didn't see eye to eye with the Confederates.
It was Lincoln who was the disciple of Jefferson, not the Confederates who rejected all that Jefferson stood for.
Stephens, Rhett, Atchison, Toombs - and even their ideological godfather Calhoun - advocated an ideology specifically based on race, not on universal natural rights like Jefferson, Washington and Franklin.
The whole notion of "states rights" (an oxymoron) was a fig leaf. Just try and get a single apologist for the Confederacy to delineate which specific "rights" of any of the slave states were being violated by the federal government.
They have no concrete answer - just vague generalities.