WASHINGTON—Justice Ruth Bader Ginsburg on Monday pronounced her verdict on “The Death of Klinghoffer”: Not guilty.

The John Adams opera opened last week at New York’s Metropolitan Opera amid accusations that the 1991 work is anti-Semitic and glorifies terrorism. While former Mayor Rudolph Giuliani and former Gov. David Paterson joined protests outside Lincoln Center, Justice Ginsburg took her seat inside.

“It...