SYDNEY—An upstart milk company’s success in marketing a controversial type of milk that is supposed to be easy to digest has some big dairy companies setting aside their skepticism to introduce their own versions.

New Zealand-based Fonterra Co-operative Group Ltd.—the world’s biggest dairy exporter, which sells Anchor butter and Mainland cheese in the U.S.—said in February it would start producing A2 milk, which contains only the A2 beta-casein protein, after years of dismissing it as a gimmick. That same month, Nestlé SA...