Democrats, as they were configured at the time. Since then, the only vestige of that era left on the party is the name “Democrats”. The party itself bears no resemblance at all to the party of that era.

It should be noted that the alignment between Republican and Democrat wasn’t a bold, clear line. The Republican Party emerged from a coalition of frustrated free-soilers, wandering Whigs, and disillusioned northern Democrats. And note that the party didn’t oppose slavery on moral grounds, but on economic and political ones. 
Actually they were rich white southern jerks, just like rich Republican Politicians are now. Look up the climate denier 1% tax break giving incomes, benefits and multimillion dollar net worth's! I've voted or a few Republicans in my time including Nathan Deal. I just voted for the better person for taking care of the country not them selves