We must remember that American culture in the twenties proceeded in relative isolation. American involvement in World War I was itself short and limited, known largely by the accounts of those who came back (and unfortunately, the loss of those who did not). Stateside, the Roaring Twenties still proceed, with Art Deco, Dadism terra cotta facades, flapper dresses, silent movies, Model T’s, etc. If prohibition does not outlaw beer and wine, organized crime does not blossom and the Cosa Nostra remains a relatively obscure family alliance arrangement among Sicilian immigrants.
Now, women can vote in all elections in all states. Fashions will “open up.” Now, what about night clubs. Before prohibition, many taverns were off limits to women. Some had troughs in front of the bar for spit and urine. Some communities had laws that prohibited women from entering “tippling houses” or “dram shops.” When all liquor moved to the secret “speakeasies,” the rules all disappeared. As for the ATL social scene, it will likely loosen, but more slowly.
What about Europe? With no WWI, we can assume that border tensions have been mutually settled (Germany/Belgium, Alsace-Lorraine, etc.). Moreover, millions of people will still be alive, contributing to a growing world economy. Of course, the German economy, and the Deutschemark, will not collapse in 1923. In OTL, World War I voided German patents and trademarks. Aspirin will remain a trademark of the Bayer company. Moreover, the Haber process for fixing atmospheric nitrogen into nitrate fertilizer would remain under German patent into the twenties. That could restrict the availability of electricity worldwide. How? The only other viable industrial process for fixing atmospheric nitrogen was the carbide-cyanamide process developed by Norsk-Hydro. No longer under patent, it consumed tremendous amounts of electricity to make fertilizer. With power grids coming on line to distribute hydroelectric power, competition might develop.
As for music and entertainment, it would change little. The big quantum leap in entertainment technology comes at the end of the decade when sound comes to motion pictures.
I would say the net result worldwide is a somewhat more prosperous twenties, worldwide. What happens afterwards is probably more significant, but the subject of this thread is the twenties.