When Anna Netrebko appeared in full old-fashioned geisha get-up at the recent gala concert celebrating the Metropolitan Opera’s 50th anniversary at Lincoln Center, you didn’t need to look at your program to know that she would be performing “Un bel dì,” the most recognizable aria from Puccini’s “Madama Butterfly.”

Ms. Netrebko’s dramatically contoured eyebrows, black wig adorned with kanzashi (ornaments) and stylized arm and hand movements paid homage to traditional stagings of this beloved 1904 opera, which revolves around Cio-Cio San, a Japanese teenager who is seduced and then abandoned by a caddish American naval officer. But opera is going through a broad reassessment of the way its classics, almost all conceived by Western men, have regularly portrayed Asia.

The kitschy, kimono-clad white actors who have often been cast in Gilbert and Sullivan’s “The Mikado” have stirred outrage in recent years, setting off a debate about whether that 1885 piece can be acceptably presented to a modern audience. The gaudy Orientalism of another Puccini crowd-pleaser, “Turandot,” set in an imaginary ancient China and featuring three ministers named Ping, Pang and Pong, has also been criticized. “Butterfly,” an opera based on a short story and subsequent play, helped perpetuate the modern Western stereotype of the obedient, long-suffering Asian woman. “Love me with a little love,” Cio-Cio-San sings at one point, because “we are a people used to small, modest and quiet things.”

“Pieces like ‘Madama Butterfly’ tend to be frozen in time: in the way they’re presented, in the way people expect to receive them,” said Daniel Schlosberg, the co-music director of Heartbeat Opera, a small New York company that will be presenting four performances of a radically revised and trimmed 90-minute “Butterfly,” from Saturday through May 28 at the Baruch Performing Arts Center in Manhattan.