That's the liberal chant, that conservatives are just like Confederates who wanted "States rights".

NO. The liberal view is that the South rewrote history so that the war wasn't about slavery, but about state's rights. Which is what happened. It's part of the Lost Cause mythology.

State's rights became a code word or a dog whistle:

"Since the 1940s, the term "states' rights" has often been considered a loaded term or dog whistle because of its use in opposition to federally-mandated racial desegregation[42] and, more recently, same-sex marriage and reproductive rights.[43][44]

During the heyday of the civil rights movement, defenders of racial segregation[45][c] used the term "states' rights" as a code word in what is now referred to as dog-whistle politics: political messaging that appears to mean one thing to the general population but has an additional, different, or more specific resonance for a targeted subgroup.[46][47][48] In 1948 it was the official name of the "Dixiecrat" party led by white supremacist presidential candidate Strom Thurmond.[49][50] Democratic Governor George Wallace of Alabama, who famously declared in his inaugural address in 1963, "Segregation now! Segregation tomorrow! Segregation forever!" later remarked that he should have said, "States' rights now! States' rights tomorrow! States' rights forever!"[51] Wallace, however, claimed that segregation was but one issue symbolic of a larger struggle for states' rights. In that view, which some historians dispute, his replacement of segregation with states' rights would be more of a clarification than a euphemism.[51]: wiki