Progressives Stay with Republicans
If Theodore Roosevelt had not challenged Taft in the 1912 election or Wilson had not been able to claim the mantle of progressivism, it is possible that progressive movement could have been the majority in the Republican Party. If Roosevelt had not divided the vote and left Taft had won in 1912, Progressives could have continued to push Taft or gathered their strength in the party and chose a candidate to their liking in 1916 or 1920. Progressives could have stayed relevant for a bit longer without Wilson's failures or Roosevelt's division of the Republicans. Progressives like Robert La Follette could have had greater influence in the Republican leadership. The Democrats, on the other hand, could have remained a conservative party in the style of Grover Cleveland if progressive leaders had been margianalized or separated from the Democrats. The conservative Deep South could have a great stranglehold on the message of party and possibly gather conservative rural voters in the West or Midwest disaffected from the progressive Republicans. Democrats could lose voters in the Northeast if Republicans appealed to these urban voters by focusing less on a Protestant-only message. If Democrats and not Republicans had advocated for Prohibition, then these wet urban voters would have only joined Republicans and the Democrats would have soldified the conservative rural voters. I suspect that the Republicans could have been socially moderate and economically progressive with voters in the Northeast, Rust Belt, and the Left Coast, and the Democrats could have become socially and economically conservative with voters in the South, Greater Appalachia, and the Western States, while the Midwest becomes the swing vote.