When Michelle Terry, the artistic director at Shakespeare’s Globe theater in London, decided to put on a production of “Richard III” with a feminist twist, she probably didn’t expect accusations of discrimination. But that’s what she got. The run-up to the show’s premiere on Tuesday was overshadowed by a controversy over the fact that Terry had cast herself as villainous title character despite not having a physical disability.

The play depicts a set of murderous machinations whereby Richard, Duke of Gloucester, achieves his ascent to the English throne in 1483, and the events leading to his demise at the hands of Henry, Earl of Richmond, who would become Henry VII, the first Tudor king. Richard, described as “deformed” in the play’s opening lines, has traditionally been portrayed as a hunchback — almost always by able-bodied actors, with only a few notable exceptions in recent years. (In 2022 Arthur Hughes, who has radial dysplasia, became the first disabled actor to play Richard for the Royal Shakespeare Company.)

When Shakespeare’s Globe announced its casting earlier this year, the Disabled Artists Alliance, a British organization, published an open letter condemning it as “offensive and distasteful,” since Richard’s “disabled identity is imbued and integral to all corners of the script.”

Shakespeare’s play, the statement added, “cannot be successfully performed with a non-physically-disabled actor at the helm.” The Globe issued a robust response pointing out that Richard would not be played as disabled in this production, and adding that, in any case, “the Shakespearean canon is based on a foundation of anti-literalism and therefore all artists should have the right to play all parts.”

Until relatively recently, it was uncontroversial to have a nondisabled actor play a disabled role. Dustin Hoffman’s portrayal of an autistic character in “Rain Man” and Daniel Day-Lewis’s protagonist with cerebral palsy in “My Left Foot” both won best actor prizes at the Academy Awards in the late 1980s. These days, the practice is increasingly contentious: Jake Gyllenhaal received blowback when he played an amputee in “Stronger” (2017), as did Dwayne Johnson in the action movie “Skyscraper” (2018); Bryan Cranston was similarly criticized for playing a quadriplegic in “The Upside” (2019).