Class is the defining concern of the play. Yank is a member of the working class, exploited for little money and with next to no chance of ever moving upward on the social ladder. The industrialized nature of the work he does forces him to become machine-like and subhuman in the eyes of the higher-ups. Mildred is the daughter of a successful businessman, privileged and secure, but she too is limited: she feels her life is meaningless and dull, and she wants to glean some kind of fulfillment from meaningful work.
The class conflict kicks into gear when Mildred sees Yank and is frightened of his beastly appearance. She calls him a "filthy beast" and faints. This awakens great rage and alienation within Yank, who loses his feeling of importance in the running of the ship where he works. He resents the upper classes, but also learns he does not entirely belong with the lower orders either as he makes his journey through Manhattan. The social order has effectively dehumanized him.
Class conflict is one of the basis of the play, "The Hairy Ape" if you look at Yank as the epitome of the lower class, he works incredibly hard but reaps no benefits, only those who own the machines get an benefits from Yanks' hard work. It is this seed of discontent that begins Yank's transformation into one of the disillusioned. Mildred and her family are the embodiment of those who are exploiting the workers in the play.