Arthur Miller is my favorite American playwright by far. I also have a special appreciation for his powerful drama “All My Sons,” which came to Fort Lauderdale’s Parker Playhouse in the 1970s when I was covering theater there for The Miami Herald. Jack Klugman headed a strong cast in the principal role of Joe Keller. I was privileged to interview Klugman at the time.

Miller’s play tells the story of the Kellers and the Deevers, two neighboring families in Ohio in 1947 whose positive — it’s fair to say loving — relationship is threatened by a scandal that won’t go away.

The play grabs my attention today because I read in The New York Times that Gregory Mosher, director of its revival on Broadway, has quit over a racial issue. Mosher had cast an African American actor to play George Deever, a principal character, and was searching for an African American actress to play the role of George’s sister, Ann. The Kellers are white. So is Mosher.

Rebecca Miller has a problem with this. Ms. Miller, a screenwriter and movie director, is the daughter of playwright Arthur Miller and presides over her father’s estate. She argues that a romantic dimension in the neighbors’ relationship would not be credible in 1940s rural Ohio. Quoted in The Times, she said, “My concern was that to cast the Deevers as black puts a burden on the play to justify the relationship in the historical context.” Since her father’s script doesn’t deal with race, she worries that casting black actors to play one of the families “would whitewash the racism that really was in existence in that period.”

Ms. Miller has supported the casting of African American actors in roles usually played by whites in other instances. The Times cited a 2019 production of “Death of a Salesman” in London that will feature a black actor in the principal role of Willy Loman. Ms. Miller is not advocating colorblind casting but rather being more conscious, not less, she told The Times. She added that she could be open to a production of the play with a black Deever family sometime in the future.

But she and director Mosher could not reach an agreement on the casting of this current production, and he withdrew, to be replaced by Jack O’Brien, a Tony-award winning director. Mosher, an acclaimed director and producer who chairs the theater department at Hunter College, is disappointed but not bitter, he said. “Man, I wanted to direct this play,” he told The Times. “It’s so good.” “All My Sons” is not a documentary about life in rural Ohio in 1947, he said. “It’s a play.”

“All My Sons” first opened on Broadway in 1947, directed by Elia Kazan, ran for more than 300 performances, and won the New York Drama Critics Circle Award. It also won the Tony for best author and best direction of a play. If you ever get to see a production of it, I highly recommend it. It’s one of a great playwright’s best plays.