Yes. Popular falsehoods perpetuated by the alt-right and neoconservatives is that the party switch never happened and that the democrats invented the KKK. The democratic party around the time of the civil war was divided into the northern democrats (center-left) and the southern democrats or "dixiecrats" (far right). The republicans of the time were the left-wing party based on their progressive ideals. It was the Confederacy that formed the KKK, and those that gravitated to the Klan happened to be the dixiecrats.
The schism in the Democratic party between the center-left Northern dems and the far-right dixiecrats persisted long after the Civil War. With the passage of the civil rights act by a democratic administration, the dixiecrats left the democratic party for the other major party, the Republicans, and took their white supremacist poison with them. This drove the liberal elements of the Republican party (the ones which held to the values of the “party of Lincoln”) to the major party which held to those values, the northern Democrats.
The KKK aligns with the right-wing party which best matches their ideals, and that, today, is the Republican party. Not all members of the GOP are klansmen, but they now have this poison in their ranks.
https://www.dallasnews.com/news/education/2017/02/02/texas-students-salute-trump-yell-heil-hitler-during-senior-photos/
https://www.youtube.com/watch?v=G24Giil9FUM
https://www.youtube.com/watch?v=1o6-bi3jlxk
https://www.youtube.com/watch?v=4i1bGq4zfzw