Historically they were originally the armed wing of the Democratic Party. They made their bones murdering Republicans in the south.
They have always been Democrats. “One” tried to run in recent years as a Repub and was hounded out by other Repubs. Traditionally they were always Democrats.
Democrat senator Byrd was a Klan recruiter back in his younger days.
Now that is interesting. It’s funny that the prevailing myth up here is that Klan people are right wing extremists. Obviously not the case.