I don't think whether or not parties switched matters or who freed the slaves matters. Things may be politically separated when they happen, but after some amount of time, all that matters is that something changed in America. It definitely doesn't matter which party did things over 100 years ago because people change, issues change, and parties change.

That being said, the political parties did swap, at least geographically. So unless my history books were wrong and the south was fighting the north to end slavery, they parties did actually switch. And here is some pretty clear proof of that.

However, that link more shows that our political alignments change all the fucking time, so its far more important what you're voting for now. Not what your vote would have represented 20, 50, 100 years ago, because I can guarantee you, your party has changed drastically since then regardless of who you're voting for in 2016.