Good point, and sorry for the oversimplification.
Ku Klux Klan (I'll explain that one later)
Yeah, from vestiges of the Civil War, right? The Democrats used to be the party of unreconstructed Southerners, due to the South's bitterness at the party of Abraham Lincoln. Stayed that way until Nixon's "Southern Strategy", which largely gave us the political map we see today.
Actually, not vestiges of the Civil War
Also, today's Republican Party is not the "party of Lincoln", because Lincoln was for big government, abuse of governmental power, and hypocrisy.
But, no, in Alabama in the 1920s, the Ku Klux Klan served as a perfect fit for the liberal coalition, because well, prohibition, which was the main moral cause of the time, was a cause that was embraced by those who also sought economic reforms to dislodge the old Bourbon alliances from power. In a strange irony of history, one study in the 1920s found that the majority of labor union members in Birmingham also belonged to the Robert E. Lee Klan
Also, many of the "moral perversions" that the Klan of the 20s railed against were primarily practiced (outside of Mobile) by those who were of a higher social class, in other words, the "moral revolt" of the 1920s was also a class revolt, and in this state, the Klan would actually attack it's opponents with all the usual Klan charges, but also with charges that they would take away textbooks from children, and all the other liberal tripe about making it hard on the poor.
It's no coincidence that the big government liberal of the time, Bibb Graves, had served as the Grand Dragon for the state, it was for this same reason that Hugo Black joined. What would become this state's New Deal coalition in this state had it's roots in the politics of the 1920s, and that included the Klan.