The Ku Klux Klan was not originally founded as a terrorist organization. It was intended to be a secret society to make fun of secret societies, and not the first. I regard the organizational history as too contingent to be likely to travel across into our alternative history.
On the other hand, night riders were so universally a part of the post-war South that I can't imagine that a slightly more forceful defeat would have kept them from arising. Even before the Civil War there were political gangs who robbed the Post Offices of mailed abolitionist literature.
The KKK were not the only white terrorists during Reconstruction, and I chose the Knights of the White Camelia, a large group, to be the most prominent group in the alternative history.