They can always argue, "what's in the name?" The 'roles' seem to be exchanged. After all, nowadays the South is Republican strength, and those places that used to be the bastion of Republican party slowly turned Democrats. I wonder if at one point Republican was seen as the 'progressive, liberal' party in social issue, while Democrat was the more conservative one. On economic issue, the roles seem the same as today, I think.
The Republicans have stood for the mostly same things throughout the years. Equality for everyone. It's the Democrat party that has swung wildly from extreme conservative (KKK Reconstruction years) to extremely liberal today. They went from NO equality for African-Americans to MORE equality for them than anyone else (affirmative action). Ever since the GOP was established the Democrat Party has tried to find a place to fit in. From disgruntled Southerners in the 1850's to 1950's to disgruntled anti-Americans from the Vietnam Era to present.