Likewise the KKK is clearly a leftist organization. Robert C. Byrd is a notable example. More recently, Frazier Glenn Miller ("Frazier Glenn Cross"), the murderer in Overland Park, KS was a staunch DemonRAT. And of course, the Westboro goons were headed by Fred Phelps, a liberal "civil rights" lawyer and backer of Al Gore.
Scratch a real racist and you'll find a leftist...every single time.
I know they were radical-populist Jeffersonians, and I think Jefferson might have disapproved of them if he'd lived, say, another 40 years. But when you stop to think of it, their "racism" was actually populism dressed up in rags tailored for them by the Communist Left -- "sad rags" as opposed to "glad rags", you might say.
And if the Klan were populists who rejected blacks as members of another, rival populus/People, then like the Bolsheviks who talked about narodny this and narodny that, and the Nazis who talked incessantly about their Volk and did everything they did in their Volk's name and for their benefit, then therefore the Klan was likewise a populist-Leftist group.
This, of course, assumes that they actually think about anything. A lot of Nazi beer-hall thugs didn't, but that didn't stop them from being Nazis and therefore Leftists.
One of the major polemical black-propaganda themes of the Communist movement over the last 70 years has been to use their rhetorical paint-box to separate themselves from other Leftists either a) behaving badly (like the Paris Commune) or b) competing with, and even waging war on, the CPSU and the Soviet State. The latter would include Trotskyites, Nazis, and "yellow" Eurosocialists.