WASHINGTON—A reflective Justice Ruth Bader Ginsburg offered something of a lament Saturday night for the polarized state of national politics, speaking to a theater audience following a play about her late friend and ideological sparring partner, Justice Antonin Scalia.

The court’s senior liberal justice was on hand at Arena Stage in Washington, D.C., for a new run of The Originalist, named after Justice Scalia’s method for interpreting the Constitution according to its perceived original meaning. The play centers on a fictional...