At a brewers’ conference this spring, an alcohol lobbyist fired a warning shot in what has become a multimillion-dollar global battle. Public-health officials “want to tell you that alcohol causes cancer,” Sarah Longwell, managing director of the American Beverage Institute, told the crowd. The industry, she said, was in danger of losing its “health halo.”

For decades, beer, wine and liquor producers have been helped by a notion, enshrined in a number of governments’ dietary advice, that a little alcohol can provide modest...