There were no political parties in the Confederacy. Their elected officials were a mix of Democrats and former Cotton Whigs.
CSA VP Alexander Stephens, famous for his Cornerstone Speech, was typical of Southern politicians of the day:
"Despite his late arrival in the Democratic Party [1854], Stephens quickly rose through the ranks.
He even served as President James Buchanan's floor manager in the House during the fruitless battle for the slave state Lecompton Constitution for Kansas Territory in 1857.
He was instrumental in framing the failed English Bill after it became clear that Lecompton would not pass, in order to negotiate its approval."
The US Civil War was Democrats waging war against the United States, a war which Democrats continue to this day.