It should be noted that the KKK took over the state government in Indiana in the 1920s, supporting Republicans including the governor. To my knowledge that’s the only case where the Klan was tied up with the GOP.
The Klan penetrated both parties in Colorado in the 1920's, but most deeply into the Republicans. In 1924 they elected a nominally Republican Senator and Governor. It was a rather brief era and both were turned out in the next election. A multiple term Democrat Mayor of Denver, Ben Stapleton, began his career with Klan affiliations and support.
Strongly Republican El Paso County (Colorado Springs), backed by Republican leaders, kept the Klan out.