Representatives for Mr. Barris, ABC and Netflix declined to comment.
A split would mark another high-profile departure for ABC. Ms. Rhimes, the force behind “Grey’s Anatomy,” “Scandal” and “How to Get Away With Murder,” decamped for Netflix last year. But ABC also has a degree of strength that it hasn’t had in years, thanks to the revival of “Roseanne,” which has scored blockbuster ratings in its first two weeks. ABC also has a new hit drama, “The Good Doctor,” and its reboot of “American Idol” has performed solidly.
Ever since Netflix poached Ms. Rhimes and Mr. Murphy, many star producers in Hollywood have been expressing some resentment that they do not have similar deals.
“Black-ish,” which is in its fourth season, has been a standout comedy for ABC, praised for its nuanced approach to race relations. It has earned a Golden Globe Award for one of its cast members, Tracee Ellis Ross, as well as a Peabody Award.
In the shelved episode, Dre, an advertising executive played by Anthony Anderson, raised socially fraught issues while telling a bedtime story to his baby son, Devante.
“Dre is on baby duty for the night during a storm, and the household is wide-awake,” ABC declared in a news release before the show had been pulled. “He decides to read a crying Devante a bedtime story, but when that doesn’t do the trick, Dre tosses it aside and begins to tell a story of his own about the current state of the country in a way Devante will understand.”
Mr. Barris co-wrote and directed the episode, which reportedly was also going to examine the National Football League’s “take a knee” protest.
It is rare for an episode to be pulled, especially in a series as important to a network as “black-ish.” At the time, ABC and Mr. Barris papered over their tensions with bland pronouncements.
“Given our creative differences, neither ABC nor I were happy with the direction of the episode and mutually agreed not to air it,” Mr. Barris said in a statement last month. “‘Black-ish’ is a show that has spoken to all different types of people and brought them closer as a community and I’m so proud of the series.”
In its own statement, ABC said: “One of the things that has always made ‘black-ish’ so special is how it deftly examines delicate social issues in a way that simultaneously entertains and educates. However, on this episode there were creative differences we were unable to resolve.”
Mr. Barris, who also has a hot movie career, co-writing the script for “Girls Trip” and a coming remake of “Shaft,” canceled an appearance at a South by Southwest panel in Austin, Tex., the day after the news surfaced that the episode would not air.
Making matters more complicated at ABC, the most recent episode of “Roseanne,” which more than 15 million people watched on Tuesday, included a glib exchange about “black-ish” and another ABC sitcom, “Fresh Off the Boat,” which is about an Asian-American family.
In the middle of the episode, Roseanne Conner (played by Roseanne Barr, the show’s star and co-creator) and her husband, Dan (John Goodman), fall asleep on a couch with the TV on. When Roseanne wakes up, she remarks that they slept all the way from “Wheel of Fortune,” the syndicated game show that airs before prime time, to “Jimmy Kimmel Live!,” the ABC late-night show.
“We missed all the shows about black and Asian families,” Dan remarks, to a chorus of laughs from the “Roseanne” studio audience.
“They’re just like us,” replies Roseanne, who grabs the remote and turns off the TV. “There, now you’re all caught up.”
The reboot of “Roseanne” was one result of an attempt by ABC to appeal more to Middle America in the wake of Donald J. Trump’s 2016 election win. That strategy is what helped persuade the network to schedule “Roseanne,” an ABC hit from 1988 to 1997 that features a white working-class family in Illinois.
“We had spent a lot of time looking for diverse voices in terms of people of color and people from different religions and even people with a different perspective on gender,” Channing Dungey, ABC’s entertainment president, said in an interview last week. “But we had not been thinking nearly enough about economic diversity and some of the other cultural divisions within our own country. That’s been something we’ve been really looking at with eyes open since that time.”
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