Yes. They believe the Civil War was really about states' rights and independence from Federal authority, and that slavery was just an incidental part of that greater struggle, and that their culture represents the last strain of "pure" (politically, not racially, but also kind of yes racially) American culture reflecting the original intent of the founding fathers, before the Federal government started its slide into totalitarianism.
It's a lie, but like all effective lies, it's half-baked in truth. Yes, the Civil War was about states' rights... the right of states to own slaves. Yes, Southern forces fought, often valiantly, for their independence... from anti-slavery laws. Yes, there were issues other than slavery, specifically, that caused the South to secede. Every one of those issues inevitably intersects with the institution of slavery at some point.
The lie is that it's possible to somehow extract Southern culture from its racist roots, as if slavery and its legacy can just be ignored and set aside as not really pertinent, when slavery was as foundational to the South and its culture as anti-Semitism was to the Nazis.
Sure, Hitler designed the VW Beetle and the Nazis built the Autobahn (but not entirely), but that's no reason to fly the swastika in your window.