Shakespeare often utilized racist, anti-semitic, and sexist language in his poems and plays. If women and minorities cannot read a work without being offended, it cannot be universal. "The Merchant of Venice" is Shakespeare's biggest offender, where he indulges in the Jewish caricature of Shylock as his main villain . He utilizes stereotypes about moneylending and greed to dehumanize the character, and people as odious as the Nazis have weaponized these stereotypes in performance of the play. His other works frequently feature lines which discuss women as sexual objects or as essentially different than men. He also frequently has characters refer to darker skin as if it is inherently ugly or makes one evil. In "Othello," the dark-skinned protagonist brutally murders his wife 
Both Shylock and Othello are characters Shakespeare wrote to be deeply sympathetic. The most famous speech from The Merchant of Venice deals with Shylock's innate humanity, and Othello was manipulated by Iago.
[P1] Bigoted writing offends readers who identify with the targeted groups. [P2] Shakespeare's writing was bigoted.
Rejecting the premises
[Rejecting P1] Thoughtful readers can engage with bigoted writing without being personally offended. [Rejecting P2] Shakespeare wrote bigoted characters, not bigoted works.