Over the past two decades, Bryan Singer’s films—The Usual Suspects, Valkyrie, Superman Returns, four of the X-Men movies—have earned more than $3 billion at the box office, putting him in the top tier of Hollywood directors. He’s known for taking risks in his storytelling: It was Singer’s idea, for instance, to open the original X-Men movie with a scene at Auschwitz, where a boy uses his superpowers to bend the metal gates that separate him from his parents. Studio executives were skeptical about starting a comic-book movie in a concentration camp, but the film became a blockbuster and launched a...