If Lincoln was alive today he would be a Dem. The partys changed control many times and also names part of the way.
I grew up in Wilmington NC. Wil had race riots a long time ago. What happened was blacks all shifted to the Republican party and took control and put in some people that would help them. Needless to say a large % of whites did not like that and riots broke out.
A party name is just that, a name. Its who controls it that matters.