The Beer and Whiskey League, officially American Association (1882-1891), was created to compete against the National League (NL) which was viewed as prude.
In the late 1800s baseball was becoming a national interest and because of that was the subject of political dispute as to its limits. It became representative of the conflict between nativist Americans and immigrants.
Nativists in the baseball represented by the National League did not want alcohol sale in the ballparks nor games on Sundays. On the other hand, for many people, especially German and Eastern European immigrants alcohol and Sunday games were an essential part of baseball.
Because of this conflict brewers and distillers in Louisville, Cincinnatti, and Pittsburgh, cities with large populations of immigrants, created the American Association. For these people, beer and baseball was an important part of their cultural lives.
In this period its clear how nativists and immigrants fought for their different views on baseball accordingly to their cultural framings. For many decades yet the association between immigrants and alcohol would be used by racist nativists against immigrant populations.
The answer is education reform