During WWI propaganda and a heightened sense of xenophobia (fear of foreigners) made many Americans uncomfortable regarding the changing face of the nation. During the 1920's Woodrow Wilson's Attorney A. Mitchell Palmer used the Justice Department to raid any group he deemed as suspicious. Adding fuel to the Red Scare this policy referred to as Palmer raids only served to increase the tension between immigrants and labor groups in the U.S. which is what led to the resurgence of the Ku Klux Klan during the 1920's. Their increased presense was such that they were influencial in pressuring the Congress to pass the National Origins Act in 1929.
The emergence of a growing sense of liberal or changing ideas helped to bring back the traditionalist approach of the KKK. The previous post correctly identified the liberal immigration policy that helped to bring the KKK into emergence. This can be extrapolated into a larger context of the time period, which embraced liberalism in conduct and social perception. The Prohibition Era's rise of gangster and an underworld culture, as well as the social emphasis of flapper culture were also reasons that individuals felt that the social compass was spiraling out of control. The growth of new voices such as women and people of color helped to bring about a sense in America that "traditional" values were being cast aside. It is because of this that the rise of religious revivalism in some areas and a separate rise of the KKK sought to bring a "traditionalism" into a setting where little was traditional.
The issue that led to the KKK coming back into power was immigration. The KKK got back into national prominence because people were upset about how much immigration there was.
We think of the KKK as an anti-black organization, but in these days, it was mainly anti-immigrant, anti-Catholic and anti-Jew.
The US had had a pretty liberal policy on immigration in those days, letting just about anyone in as long as they were not Chinese. By the 1920s, this meant that there were a lot of immigrants in American cities. Many of them were Italian Catholics and Russian and Polish Jews.
They seemed too foreign and their coming happened around the same time as things like the flappers. Traditionalists in rural areas put the two together and supported the KKK in its attempt to bring back a more traditional, rural, protestant Americanism.