You mean more than have Woodrow Wilson as President and have Harding inducted to the KKK while president?
You might want to look at the events that killed the Klan as a political force--something about some sick bastard raping and cannibalizing a woman, and making a huge mockery of the supposed values of the KKK.
That said, the easiest way for this to happen is to have a botched reconstruction and the KKK becomes a massive paramilitary organization...