This was all brought to mind by this article at New Republic that first sounds a bit light weight: How the Klan Got Its Hood - but in the course of the explanation, it looks at this matter of the openness with which people could support the movement.
It is very startling to read things like this:
Lynchings were not spontaneous outbursts of “mob” violence, but the predictable result of institutional support and the outright participation of political elites. The lynchers of Leo Frank, in Marietta, Georgia in 1915, included a former governor, judge, mayor and state legislator, sheriff, county prosecutor, lawyer and banker, business owner, U.S. senator’s son, and the founders of the Marietta Country Club. Frank’s atypical case—he was white and Jewish—attracted media attention that thousands of black victims never received, yet it exposed the ways that elites and authorities exonerated themselves by blaming mob violence on so-called “crackers.” Meanwhile, Mississippi governor, later U.S. senator James K. Vardaman said in 1907, “If it is necessary every Negro in the state will be lynched; it will be done to maintain white supremacy.”And to read the horrifying details of some lynchings:
Vardaman didn’t wear a white hood. Neither did the first woman U.S. senator, Rebecca Latimer Felton, who said in 1897, “If it takes lynching to protect woman’s dearest possession from drunken, ravening human beasts, then I say lynch a thousand a week if it becomes necessary.” They were cloaked, instead, in state power and popular support, and what their platforms concealed was the truth: Wells-Barnett’s reporting and the National Association for the Advancement of Colored People’s (NAACP) research had disproved the “thread bare lie” of the lynch mob as honorable defenders of white women. Besides the fact that the myth of the black rapist was a white supremacist fantasy, 70 percent of lynchers didn’t even bother to invoke it to justify their violence. Lynchers killed for such alleged offenses as “sassing,” wanting a drink of water, being “troublesome,” “conjuring,” and often, as in the murders of Mrs. Jake Cebrose and an eight-year-old child named Parks, no excuse at all.
In 1918, Georgia governor Hugh M. Dorsey wrote to the NAACP, “I believe that if the negroes would exert their ultimate influence with the criminal element of their race and stop rapes that it would go a long way towards stopping lynchings.” The “criminal element” he was referring to was Mary Turner, who had threatened to press charges against the lynchers of her husband, Hayes Turner, and of nine other men. The lynchers, as reported by the Savannah Morning News, “took exceptions [sic] to her remarks as well as her attitude.” They lynched Mary, who was eight months pregnant. Journalist Walter White, whose ability to pass as white enabled him to interview the murderers themselves, reported that they had hung Mary upside-down, set her on fire, cut out her fetus and stomped it, then shot Mary’s body multiple times. The Brooks County coroner’s jury ruled that all the victims had died “at the hands of parties unknown” and closed their cases; a lyncher served as jury foreman.But back to the question in the title of the New Republic article: it appears Hollywood, in the form of Birth of a Nation, as well an enterprising mail order business, gave the Klan its "classic" look.