Question

How progressives saw their role in the debate over prohibition of alcohol

Answer 1

progressives saw their role as protecting the social moral and they viewed alcohol consumption led to crime, health, family and other social issues. so they supported the Prohibition. their positions turned out to be wrong as Prohibition caused more crimes even though alcohol consumption went down.

Answer 2

The question did not specify but presumably it refers to the social progressives during the time of Prohibition of alcohol in the US.

The progressives supported the prohibition as they considered alcohol the cause for social issues such as family violence, alcoholism and corrupted politics. So they and the Protestants pushed for the Prohibition as a social moral and health issue.