Dripping with sexism and class snobbery, “My Fair Lady” is one of those musicals so grating to 21st century sensibilities, one might feel it should remain on the shelf. Ah, but the Lerner-Loewe tunes are magnificent. And any tale that’s persisted from Greek mythology to Shaw’s “Pygmalion” to “Pretty Woman” clearly touches deep psychological chords.

Enter Bartlett Sher, whose “My Fair Lady” shifts the story’s focus from its Pygmalion, the arrogant Henry Higgins, to Eliza Doolittle as a smart, scrappy woman who insists on dictating the terms of her own life.