Nope from the beginning the Civil was over slavery no matter what they taught in Virginia. In a sense you actually got this backward - It's true that states rights was the reason why some of the later states seceded (Virginia), and was the reason many (probably most fought for the south) . Additionally it was the primary reason the north fought the south (the North didn't believe they had the right of secession). But the base reason South Carolina and the other fire breathing states seceded in the first place and got the Civil War ball rolling was to protect slavery.
I'll be honest I've always been a bit of an anti confederate but I'm uncomfortable with how this tearing down of statues is playing out and what it might entail. President Wilson was an unapologetic Racist, FDR set up camps for American Citizens, Jackson (and the Army for that matter) crapped all over the Indians etc etc. Will memorials to them, other Presidents, the famous, ect. be the next targets?