From the 1930s onwards various mob groups clearly had massive influence in the industry. They had been brought in by the studio bosses to infiltrate the unions, and also to head off competitors. By the time Scarface was made, Al Capone had a hand in the editing process. Mob influence in Hollywood output was probably greater than that of the Communist Party.
This is not to dismiss the real radical shift of a whole number of Hollywood stars and studio workers, but rather to recognise that the CP grew massively in the early and mid-1930s because of its involvement in a revived working class struggle. The Popular Front from 1936 served to undermine those struggles as the CP pursued an accommodation with top labour leaders and pushed for support for the Democratic Party.
Ordinary CP members' activity in various struggles shaped the party's impact on culture far more than the stultifying Moscow line of "socialist realism", or indeed the theory of the Popular Front.