If I remember my history correctly (probably not), the KKK was once comprised of Democrats.
Of course it was. After the War, the only Republicans down South were invaders. That old Klan was the shadow government which ran what the Yankees, Carpetbaggers, and Scalywags did not.
The Democrats managed to distance themselves from the present day Klan.
As has been pointed out, the Klan just after the War was a vigilante group, but not so much a 'hate' group. That part starts in the 1900s. Similarly, the Democrat Party changed to a largely Marxist organization in the 1960s with the advent of The New Left (if the 1930s didn't foreshadow that).
So now it seems the Klan and others like them are trying to rebrand as Republicans and/or conservatives.
They aren't Marxists, and in the world of media driven false dichotomies, that leaves the GOP. The media have been calling Republicans Nazis (recall "BushHitler" memes?), perhaps because the 'Nazis' are an enemy the Marxists can understand.
That must be the story perpetrated by lefty media such as MSNBC because I have liberal friends who are fans of MSNBC and others like them and they keep telling me that these Klan/neo-Nazi/white supremacist groups are conservative or Republican.
The media have been trying (along with groups like the SPLC) to lump everyone from the Young Republicans to the NRA to Right to Life folks and Stormfront all together in a tidy little package to hate for a very long time. It was Federal 'investigation' that led to the Ruby Ridge incident when Randy Weaver would not act as an informant on his separatist neighbors (GHWB), despite entrapment over gun charges being used as leverage by the Feds. The whole incident on the ridge was over charges of "Failure to appear" on a warrant where the date had been moved up and Weaver was notified of a different date.
The attempt to conflate people who love Jesus (and even Jews) who own firearms, revere the Constitution, believe in the Rule of Law, and the Bill of Rights with the KKK and NeoNazis has been going on a long time, but so has the media foisted ignorance of the groups involved, smeared with disinformation campaigns by the media to remove the very great distinctions.
It's exhausting to try to explain to my loved ones that they are being fed a line of BS by dishonest lefty media. These hateful people do not represent me anymore than BLM represents every black person.
Point out to your relatives the spectrum on the Left from the Communists to Antifa to BLM to PETA and the Sierra Club (I know, it's hard to find a Leftist group who aren't Communists at their core) and ask them if they think everyone over there shares anything but a disdain for the Constitution and the Rule of Law. The media present two dimensional false dichotomies for a reason. People are more complicated than that.