The end of WWII and the start of the Cold War was the beginning of the end of respectable racism because the Nazis went so overboard with the Holocaust it started people thinking about their own racism and to compete with the USSR (Which could keep its racists out of the press) in the Third World the US had to start abandoning institutional racism. A non-racist KKK is no longer a KKK.
I dont see that except a abstract sense. In the Reconstruction era the Klan was about removal of 'Yankee' intrusion & restoration of poltical power to the former southern political leaders. The white supremacy & suppresion of the liberty of the former slaves was incidental to that. The racist aspect was part of the fabric of US culture & southern politics. It would have been odd if the Klan had not reflected the culture in which it existed & it was in no way unique in reflecting the culture/politics of the era.
The Klan revival of the 1920s was focused on "morality" & immoral white Protestants were the targets of Klan violence as much or more so than Catholics who were the primary verbal target of the 1920s Klan. Prohibition was the other largest or core issue in the members motivation and the Klan was active in suppresion of illegal alcohol trade. Violence against African Americans had continued during the Klan hiatus from the 1880s to 1915 & was informally organized. It continued from the Reconstruction era into the mid 20th Century with or without Klan participation. The northern Klan, which was in some regions like New York/New Jersey larger & stronger than the southern Klan of the 1920s. Anti Catholcism and Prohibition were the near exclusive issues in those regions. there was a similar trend in the Klans of Oregon & Washington states, Colorado, California.
Race became more important in the 1930s as a Klan focus & there were actually attempts to reconcile with Catholic & Jewish groups as the protestant clergy became less active in the Klan. While the suppression of registration of black voters, black business, and Black mobility became a large part of Klan activity this was part of a larger suppression of southern labor. The Klan brought violence against union organizers equally among black or white laborers, and intimidated white voters into balloting the right way rather than complete suppression as with black voting. Suppression of the agrarian and factory laborers appears to be the primary focus of the Klan in the 1930s, tho there was a strong admiration of the racial aspects of nazi doctrines among the Klans members.
The anti union/communist doctrine continued in the Klans activites in the 1940s & it was not until the civil rights movement gained traction in the 1950s that the klans began focusing on race over the other aspects. Tho "Protestant" and religion remained a important part of the klan doctrine and argument.