The brewers and distillers knew women were the Prohibitionists' chief allies and saw the WCTU [Woman’s Christian Temperance Union] as its most formidable foe. The repeated failure of many state legislatures to bring about women's suffrage must be laid at their door.
…and why Prohibition supporters fought for women's rights (via Smithsonian magazine, an article I recommend to anyone interested in political movements):
The suffrage movement had long shared a constituency with the anti-liquor movement. Frances Willard and the WCTU campaigned actively for both causes. Susan B. Anthony had first become involved in securing the vote for women when she was denied the right to speak at a temperance convention in 1852 in Albany, New York. By 1899, after half a century of suffrage agitation, Anthony attempted to weld her movement to the Prohibition drive. “The only hope of the Anti-Saloon League’s success,” she told an ASL official, “lies in putting the ballot into the hands of women.” In 1911, Howard Russell’s successor as the league’s nominal leader, Purley A. Baker, agreed. Women’s suffrage, he declared, was “the antidote” to the efforts of the beer and liquor interests.
Prohibitionists had trouble winning with the current set of election rules, so they went out and changed the rules to empower and enfranchise their natural ally, women. Prohibitionists made common cause with women's suffragists. This long-term planning to push for legislative action helped to increase the power of the Anti-Saloon League.
Finances motivated another move. Taxing liquor was a large source of government money, so if it was ever outlawed, there would be a need for an alternative source of revenue. The income tax became that other source. The ASL helped pass the 16th Amendment to impose income tax in 1913:
This was not the only alliance that the ASL made with other movements. Though in its public campaigns it stuck to its single issue, the league had worked with Western populists to secure ratification of the income tax amendment.
Changing tax policy was a prerequisite to make Prohibition possible politically and financially. The lesson for advocacy groups: Lay indirect groundwork to ease policy transformation.
A lesson for the modern Democratic Party
The Democrats have failed to learn the lesson from the Anti-Saloon League about empowering your allies and changing the rules to enfranchise your likely voters. Democrats completely blew a rare chance this year to use their unprecedented control of the federal government to push for statehood for Washington, DC. This would probably give Democrats two Senators and one House member by enfranchising hundreds of thousands of likely Democratic voters. Instead, Democrats utterly failed, thanks in part to the power of the NRA, which has clearly learned from the ASL's success.
If Democrats want to secure their power, they should push for legislation that makes it easier for their likely supporters to vote for them. Same-day voter registration would spur infrequent voters (who tend to vote more for Democrats) to participate in elections. Hispanics have been trending Democratic, so easing the citizenship process for immigrants from Latin America should increase the pool. Equally, it has been a political failure by Democrats not to pass the Employee Free Choice Act, which could increase union membership, helping Democrats by empowering a traditional ally.