More importantly Progressivism in its zeal for top down social reform were strong supporters of Prohibition. Women at that time considered the Temperance Movement more important than suffrage.
What a screwphemism that was. Temperance didn’t mean moderation.
Part of the Temperance movement was about rabid anti-Catholicism.
Not hard to see what the Suffrage movement, with not a small number of KKK Women, might also be friendly towards the Temperance movement.