The First Klan was almost entirely Democratic.
The Second Klan, as noted above, had links to both parties.
And more recently, well ... here's David Duke:
Here's the Snopes fact-check of it: snopes.com/fact-check/lbj…
But this particular quote was almost certainly made up and, more important, has now been mobilized to wave away the hard facts of LBJ's strong record supporting the civil rights movement.
Again, take a look at this:
Again, I've tried to explaining this to @kanyewest:
LBJ responded by calling for what became the Voting Rights Act of 1965.
And again, Southern Republicans used the politics of white backlash:
Here's the Snopes fact-check again: snopes.com/fact-check/mar…
Here's a nice piece on some of the other lies spun about her: npr.org/sections/itsal…