1920s politics:
Democrats support more government involvement and liberal ideas; Republicans support shift of less government control and more conservative values. During this time many "conservative democrats" and "liberal republicans" shift parties.
During the preceding Progressive Era (1890-1920), both parties tended to favor progressive ideas. But in the 1920s, with Republican presidencies of Harding, Coolidge, and the first year of Hoover's term in office, Republicans became less progressive and more pro-business in their policies. (The question asked about the 1920s, so the stock market crash that began on October 24, 1929 would be after the time period the question is asking about.)