There are some who claim that both Warren G. Harding and Calvin Coolidge belonged to the KKK but there is only the slimmest of circumstantial evidence to support it.
I seriously doubt it.
Coolidge spoke out in favor of the civil rights of African Americans and Catholics. He appointed no known members of the Ku Klux Klan to office; indeed the Klan lost most of its influence during his term.
In 1924, Coolidge responded to a letter that claimed the United States was a "white man's country":
....I was amazed to receive such a letter. During the war 500,000 colored men and boys were called up under the draft, not one of whom sought to evade it. [As president, I am] one who feels a responsibility for living up to the traditions and maintaining the principles of the Republican Party. Our Constitution guarantees equal rights to all our citizens, without discrimination on account of race or color. I have taken my oath to support that Constitution....
On June 2, 1924, Coolidge signed the Indian Citizenship Act, which granted full U.S. citizenship to all American Indians, while permitting them to retain tribal land and cultural rights. However, the act was unclear on whether the federal government or the tribal leaders retained tribal sovereignty. Coolidge repeatedly called for anti-lynching laws to be enacted, but most Congressional attempts to pass this legislation were filibustered by Southern Democrats. Coolidge appointed some African Americans to federal office. He retained Harding's choice of Walter L. Cohen of New Orleans, Louisiana, as the comptroller of customs and offered Cohen the post of minister to Liberia, which the businessman declined.
Every Republican president has supported Civil Rights and until the 1960s, the Democrats have fought to overturn every Civil Rights law. There is very little cross over -- the vast majority of Dems believed in White Supremacy and the vast majority of Republicans fought for Civil Rights for blacks.