Cultural Marxists grew up listening to Pete Seeger or obscure punk bands. Many of them went to socialist summer camp. Many celebrate May Day. They own copies of Capital, Volume I, and they’ve read bits of it.
Cultural Marxists are not and have never been members of the Communist Party. Nor are they, typically, members of socialist parties or labor unions. The only thing they do to help to bring about the revolution is promote the growth of the capitalist economy.