Meryl Streep made news last week for playing Donald Trump in a sketch at the Public Theater’s annual gala at the Delacorte Theatre in Central Park.

Whether intended or not, her stunt was a fitting prelude to the Public’s all-female, freewheeling, politically-minded Shakespeare in the Park production of “The Taming of the Shrew,” which presents the comedy (deemed highly problematic and misogynistic by today’s standards) as lowbrow entertainment and propaganda promoting female subservience.

It is directed by Phyllida Lloyd (whose all-female productions of Shakespeare plays have previously played St. Ann’s Warehouse) with a superb cast that includes Golden Globe winner Janet McTeer, Cush Jumbo (“The Good Wife”) and comedienne Judy Gold.

Lloyd frames the play around a tacky country-western beauty pageant, with an unseen Trump-like figure praising the looks of the contestants (who then take on roles in the play). A winner is even declared at the end.

The characters are played up as broad caricatures who engage in clowning and visual gags. Jumbo’s Katherine is a spoiled, screaming child in pigtails and McTeer’s Petruchio is a cocky cowboy in a black leather jacket.

At one point, Gold, who plays an elderly suitor, chucks her character’s monologue and instead complains to the audience about how “the director of this show is a woman” and “we’ve got a broad running for president.”

You can’t blame the Public for presenting the play from a critical standpoint. Even Shakespeare framed it as a diversion for a drunken peddler, which suggests that Katherine’s submissiveness at the end should not be taken at face value. The fast-paced production, even if self-conscious and somewhat muddled, manages to be both enjoyable and outright disturbing.

Appropriately, it ends with the women letting loose to the rock song “Bad Reputation,” which was featured in the 1999 teen film comedy “10 Things I Hate About You,” which was itself a modernized version of “Shrew.”