This is, of course, why they demanded the passage of the 1850 Fugitive Slave Act, specifically intended to override state laws making return of fugitives to slavery more difficult.
The specific issue over which the Democratic Party fell apart in 1860 was southern insistence on a federal Slave Code using federal power to force slavery on occupants of territories against their will. When northern Democrats balked, southern Democrats split their party three ways, handing Lincoln the election.
IOW, southerners didn't dislike federal power at all as long as they controlled it, which they did for most of the period from independence to the WBTS. In fact, in at least those two cases they demanded significant expansion of federal power.
Nonsense!
Just because you believe in states rights does not mean there is no place for the Federal government at all. Interstate Commerce is one of the few areas in which a Federal government is necessary. That is of course if it really is about interstate business.