If I were as unfair as writer-director Mike Binder (“The Upside of Anger,” “Reign Over Me”) is to the African-American characters in his new movie “Black or White,” I’d say this project is a white filmmaker’s rationalization to have a white character occasionally say (and certainly think) the N-word while raising a black child.

That’d be too harsh an assessment, even if there’s a kernel of truth to it. The fact remains that “Black or White” frames a custody fight for the orphaned 8-year-old Eloise (Jillian Estell) between wealthy attorney Elliot (Kevin Costner) and lower-middle-class entrepreneur Rowena (Octavia Spencer) — the girl’s maternal grandfather and paternal grandmother — as a black intrusion into white terrain.

To be sure, Elliot isn’t anyone’s idea of the ideal parent. After the death of his wife (Jennifer Ehle), he takes to the bottle early and often. To tutor Eloise (and occasionally serve as his designated driver), Elliot hires an African immigrant (a winsome Mpho Koaho), who casually informs his new employer that he witnessed the massacre of his family as a young boy.

“Black or White” is full of such tonal dissonances; the academically gifted Eloise often talks like a toddler (and seems bizarrely incurious about the sudden disappearance of her grandmother), while the soundtrack’s twinkling music feels imported from a much lighter movie.

There are valid reasons why Eloise, who grew up with Elliot and his wife after her mother died giving birth to her, should stay with her grandfather, for stability’s sake if nothing else. But the film’s strategy in arguing for Elliot’s custody is to denigrate Rowena’s family — especially Eloise’s biological father, Reggie (Andre Holland), who is a drug addict.

“Black or White” gradually offers a lurid mystery regarding just how bad Reggie is, as when he attempts to extort $25,000 from Elliot. But discovering those new depths make for a disheartening experience, since they suggest that, despite Rowena’s selflessness in taking in a variety of nieces and nephews and grandchildren over the years, her family will never be good enough for Eloise.

A rousing and fair debate would have lent the film some badly needed dramatic urgency. But “Black or White” takes a side — that of the beleaguered white man. Elliot’s speeches in court are portrayed as impassioned or wryly clever, while Rowena’s attempts to express herself are presented as inappropriate outbursts.

Costner gets one rather moving and ambitious monologue about overcoming racism as a continual process, not a terminal endpoint. But by the film’s end, “Black or White” raises only one question: Is its racial-baiting disingenuous or oblivious?