In Brave New World, the World State advocates for the whitewashing of human history, in particular the gory bits of their past, as well as the parts that they consider disruptive to their continuous operation in in such a manner that everything counter to their ideology, cultural values and socio-politico-economic systems is practically erased, except from the memory of certain individuals (e.g. Mustapha Mond) who remember what the world was like prior to the World State. Mustapha Mond also keeps a collection of ancient writings in his private safe, and among these works William Shakespeare’s various works, which embody the spirit of emotional expression and individualism, both of which are taboo in Huxley’s utopia.
John the Savage, unarguably the protagonist of the novel, was raised in a culturally atavistic society that is more naturalistic, and bears a resemblance to Native American society, with values that are contradictory to the World States’ and viewed as threatening to their society and its control over it.
When he’s taken from Malpais and introduced to the World State, he’s amazed by what he sees and all his previous adopted values from the reservation (monogamy, intimate relationships, religion etc.) become conflicting and hinder his efforts to assimilate into a world that sees him as no more than the Director’s bastard and a caste-less foreigner.
John’s extensive knowledge of Shakespearean works also interferes with his assimilation, as he’s depicted as quoting Romeo and Juliet, Othello, and Hamlet among others.
When he tries to court Lenina according to his Shakespearean readings, he refuses to have meaningless sex after their first date, instead choosing to wait until he finishes courting her; this surprises Lenina, who is accustomed to promiscuity and shallow connections, as opposed to John’s preconceived notions of bonding and intimacy prior to anything sexual happening between them. John even compares himself to some of Shakespeare’s protagonist, thinking of himself as the tragic hero caught up in a world that’s not his own, but one where he wants to belong.