During the 1930s and 1940s, Parker became an increasingly vocal advocate of civil liberties and civil rights, and a frequent critic of authority figures. During the Great Depression, she was among numerous American intellectuals and artists who became involved in related social movements. She reported in 1937 on the Loyalist cause in Spain for the Communist magazine, 'The New Masses.' At the behest of Otto Katz, a covert Soviet Comintern agent and operative of German Communist Party agent Willi Münzenberg, Parker helped to found the Hollywood Anti-Nazi League in 1936, which the FBI suspected of being a Communist Party front. The Hollywood Anti-Nazi League's membership eventually grew to some 4,000 strong. According to David Caute, its often wealthy members were "able to contribute as much to Party funds as the whole American working class," although they may not have been intending to support the Party cause.