The issue is more that 'flipped' misses the point. America was a different country then.
There are always two sides to any political system: One supports a strong centralized state while the other supports decentralized power with more local control.
In the 19th century, it was the GOP for the centralized control and the Democrats for local government power. Now it's the opposite.
the republicans have done nothing for states rights. where are the republicans talking about states rights on marijuana, same sex marriage, euthanasia, etc? how many other than paul are really talking about states doing things like coining their own money? the one real exception there is the abortion issue but even then thats not really how they normally frame that.