The rhetoric of prohibition was progressive to win support, bt the core support was from Calvinistic Protestantism in both the South and the North. Prohibition is more an indication of enduring Conservatism within the GOP as opposed to Progressivism. Perhaps that stems from the understanding of the word Progressivism. Everyone wanted to advance their society, but in their own image and that is the key thing. Aside from slavery, The Republicans were a Party that wanted to take away the Irish and German's whiskey and beer, force those of whom were Catholic amongst them to read the good King James Bible in their progressive schools built to "progress society", and prevent their relatives from joining them in America. It was more a way to impose their social views through the gov't on unwilling people, hardly a progressive approach as we would understand it.
To the extent that is the case it is because of the movements toward greater social autonomy that have associated their cause with the ideas and terminology of progress. The New Left did carry on in some sense earlier views of progress as involving expression in opposition to social control, but the politically dominant expression of Progressivism in the early 20th century tended toward a more actively reforming and remolding of society. There's no reason to not identify efforts at social control as "progressive" movements, so long as we do not laden that term with a particular moral affirmation of our own values.
Prohibition cannot be identified solely with Progressivism, and their were anti-Prohibition Progressives, particularly of German or Catholic extraction and those who allied with them. Yet it's hard to deny the strong and crucial links between Prohibition and other elements of Progressive movement such as first wave Feminism.
