Under American law, the only time being pro-Nazi was illegal was when the United States was at war with Nazi Germany. Supporting the idea that the South should be given independence was never illegal even during the Civil War (persons arrested for supporting the South were not charged with a crime or prosecuted, though they were arrested under the suspension of habeas corpus, which was subsequently found to have been illegal).
One should also note that reconciliation with the defeated rebels was a key aspect of American policy, going back to Lincoln in 1865. In other countries the animosity over civil wars often lasted centuries (e.g. it was still controversial in 20th century Britain whether they could honor Oliver Cromwell, who was the “Jefferson Davis” of the British civil war). One should note (WOKE propaganda to the contrary) the even though the Germans in World War II presented strong racial arguments to American southerners including advocating a re-enslavement of Black Americans, they found no takers – the policy of reconciliation that is denounced may be a major reason why there was southern “third column” supporting the Nazis.