Hey, great question!
It depends on how you look at it. Certainly, when it comes to electoral politics, the 1920s saw a hard turn against the Progressive movement in both major parties and (with the exception of Robert LaFollette in 1924) third parties as well.
However, recent historiography has broadened our analysis to emphasize instead the 1920s as a period of conflict in American cultural politics. For the first time, the easy availability of new forms of mass media (chiefly radio and Hollywood movies) brought the culture of American cities into contact with the culture of American rural areas. (Keep in mind, the U.S had only recently crossed over from majority-rural to majority-urban in 1920, and the sides were fairly evenly matched.)
Now, it’s not like the mass media industries of the 1920s were run by radical activists – depictions of flappers and speakeasies were good business as well as challenges to traditional morality, movies that depicted frank (including non-heterosexual) sexuality and/or violence and/or crime were made for the same crass commercial reasons that rated-R movies are made today – but their ubiquity and popularity really did make them a threat to “traditional morality,” and Hollywood had good reason to fear a ginned-up moral panic, with state legislators surfing the wave of “family values” politics from the successful ratification of the 18th Amendment.
A word on that, just to finish up. One of the things that scholars have written about in really interesting ways in recent scholarship is the complicated ways that conservative movements of the 1920s interacted with modernity – whether you’re talking about fundamentalist religious movements, which couldn’t get enough of the new technology of the radio as a way to evangelize to hereto undreamt-of audiences, or the way that the “new” Klan used modern mass advertizing and fundraising methods to drive its message of traditional white anglo-saxon culture threatened by old enemies plus the new enemies of immigrants and urban modernity, etc. Which complicates the urban/rural, modernity/traditional values story a lot.
As for movements of the left…yeah, they were around. Committed activists didn’t go anywhere and there were a lot of good fights being fought throughout the 1920s. But if you were on the left in this period, you knew that you had just suffered a major defeat and were trying to hang on until the environment shifted to being more in your favor.