I
looked it up on Wikipedia, knowing nothing about their origin beyond "something something post-Confederate South".
The first summation of the first klan seems pretty generous with their reasons for formation:
The first Klan was founded in Pulaski, Tennessee, sometime between December 1865 and August 1866 by six former officers of the Confederate army[23] as a fraternal social club inspired at least in part by the then largely defunct Sons of Malta. It borrowed parts of the initiation ceremony from that group, with the same purpose: "ludicrous initiations, the baffling of public curiosity, and the amusement for members were the only objects of the Klan", according to Albert Stevens in 1907.[24] The name is probably derived from the Greek word kuklos (κύκλος) which means circle;[25] the word had previously been used for other fraternal organizations in the South such as Kuklos Adelphon. The manual of rituals was printed by Laps D. McCord of Pulaski.[26]
According to The Cyclopædia of Fraternities (1907), "Beginning in April, 1867, there was a gradual transformation ... The members had conjured up a veritable Frankenstein. They had played with an engine of power and mystery, though organized on entirely innocent lines, and found themselves overcome by a belief that something must lie behind it all—that there was, after all, a serious purpose, a work for the Klan to do."
(Do note that the guy Stevens being quoted in 1907 which is like right before the kkk comes back into style after decades of non activity)
However the more in depth article on the first generation makes it clear that just within a year or two they were terrorizing and murdering very large amounts of people:
"Armed guerrilla warfare killed thousands of Negroes; political riots were staged; their causes or occasions were always obscure, their results always certain: ten to one hundred times as many Negroes were killed as whites." Masked men shot into houses and burned them, sometimes with the occupants still inside. They drove successful black farmers off their land.
"Generally, it can be reported that in North and South Carolina, in 18 months ending in June 1867, there were 197 murders and 548 cases of aggravated assault
Klan violence worked to suppress black voting, and campaign seasons were deadly. More than 2,000 people were killed, wounded and otherwise injured in Louisiana within a few weeks prior to the Presidential election of November 1868
Which is an awful short time to turn from one jokey fake secret brotherhood to a very large amount of independent violent associations under the kkk umbrella.
So if we're being as generous as we can be without being disearnest we have a situation where a possibly jokey fake secret brotherhood (which in itself was appatently in the fashion back then, along with non-jokey secret brotherhoods, so that isn't exactly the unusual thing about it) started for non-political reasons, which is immediately transformed by the people invited into it (and by people hearing of it and sfarting their own klans) into a very non-jokey secret society with very obvious intent on influencing and shaping the South through violent and murderous means.