Both plays concern how racial stereotyping shapes identities and traps people in stereotypical identities.
In Luis Valdez's play I Don't Have to Show You No Stinking Badges!, Sonny's mother and father succumb to American stereotyping of Mexican Americans by pursuing Hollywood careers playing nonspeaking stereotypical roles as a Mexican maid, Mexican gardener, a prostitute, and a robber. The money they earn from playing degrading, stereotypical, marginalized Mexican roles ironically allows them to buy into the stereotypical white suburban American dream; they own a "comfortable, middle-class suburban tract home in Southern California," which is furnished with leather furniture, bookcases, and an expensive entertainment center, and has all the amenities including a fire place, a two-car garage, a deck, and even a swimming pool. They can even afford to send their son Sonny to Harvard to pursue a law degree, a degree they want him to pursue because they want him to have the life they never had, a true American life free of Mexican American stereotyping. Yet Sonny wants neither an American identity nor a Mexican American identity. Instead, he's determined to create his own identity by creating his own movies, free of Mexican American stereotypes; therefore, he leaves Harvard to return to L.A. in order to pursue becoming the "next Woody Allen," a famous actor, writer, director, and producer (p. 184). Yet, by envisioning himself as the "next Woody Allen," he associates himself with an American ideal of stardom that shows he is actually unable to separate himself from American identity. Sonny begins trying to make his own film, thinking he could set it in the jungles of Central America to capture his roots, yet his ending involves him threatening his parents with his father's gun and being surrounded by the police, which only recaptures the Mexican American stereotype he is trying to escape. Through Sonny's inability to find his own identity, playwright Valdez shows us the damaging extent of stereotyping: (1) it prevents us from finding true identities; and (2) it prevents us from understanding true identities.
Similarly, in David Henry Hwang's play M. Butterfly, based off of Puccini's Italian opera Madame Butterfly, French diplomat Rene Gallimard holds damaging stereotypical views about Chinese women. As a diplomat in China, Gallimard became involved in an affair with someone he believes to be a beautiful Chinese woman named Song Liling. Due to his prejudices, he believes in the stereotype of Chinese women being ideal loyal, subservient women, an idea he gets from his favorite opera, Puccini's Madame Butterfly, in which the character Cio-Cio-San, called "Butterfly," played a very gentle, subservient role. Out of stereotypical beliefs, he abuses and shames Song while affectionately calling her his "Butterfly." While behaving abusively, he fulfills the stereotypical role of the dominant white male.
Yet roles become reversed when it is revealed that Song is actually a male spy. Once Song's true nature is revealed, Song becomes the dominant and abusive one, whereas Gallimard becomes the humiliated, subservient one. He is so humiliated that he commits seppuku, suicide by self-disembowelment, while Song watches.
Like in Valdez's play, the action in M. Butterfly helps serve to show the danger and destructiveness of believing in and accepting stereotypes.