Kenya Barris, the A-list writer-producer behind the ABC comedy “black-ish,” has grown frustrated with his home network and is examining the possibility of making an early exit from his contract, according to three people familiar with the negotiations.

Mr. Barris, 43, has also begun talks with Netflix, the streaming titan that has poached superproducers like ABC’s Shonda Rhimes and Fox’s Ryan Murphy with eye-popping pay packages and promises of artistic freedom.

Mr. Barris’s deteriorating relationship with ABC stems, in part, from the network’s decision to pull an episode of the show that examined race relations in America in pointed fashion, according to the people briefed on the situation, who spoke on the condition of anonymity to discuss behind-the-scenes friction. ABC aired a “black-ish” rerun in place of the shelved episode on Feb. 27.

A critical hit, “black-ish” centers on the Johnsons, an upper-middle-class family living in a mostly white suburb. The series has increasingly embraced hot-button story lines centered on race. It has delved into police brutality, the fallout from the election of President Trump and the use of the N-word among children. In addition, Mr. Barris is the creator of a spinoff, “grown-ish,” for Freeform, a cable network that, like ABC, is owned by the Walt Disney Company.