I thought women weren't in the theater at all (officially).
Harriet’s an idiot.
Women and girls were played by young boys.
Which sometimes resulted in a boy playing a girl who was pretending to be a boy.
But there was never any doubt in the mind of the audience as to the sex of the actor.
Only those salacious Frenchies allowed women on stage. As we all know, actresses are all whores. (Actually, at the time they pretty much were.)
Come to think of it, not all that much has changed in that regard.
You are correct, and this liberal MP is an ignoramus.
Men and boys played all women's roles because women were forbidden by law from appearing on the stage.
Women were not allowed perform on public stages until 1660.
Sometimes boy actors would play the role of girls, pretending to be boys. But, no actual girls were on stage.
Harman has probably confused her Shakespeare with British pantomime — which does feature a lot of cross-dressing (with actual female actors on stage too).