If I were as unfair as writer-director Mike Binder (“The Upside of Anger,” “Reign Over Me”) is to his 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. And the fact remains that “Black or White” frames the custody fight for the effectively orphaned eight-year-old Eloise (Jillian Estell) between wealthy attorney Elliot (Kevin Costner) and lower-middle-class but hyper-entrepreneurial Rowena (Octavia Spencer) — the little girl’s maternal grandfather and paternal grandmother, respectively — 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 ensure Eloise completes her homework (and to serve sometimes as his designated driver), Elliot hires an African-immigrant tutor (a winsome Mpho Koaho), who casually informs his new employer during their first meeting 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 several 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 her drug-addicted son (and Eloise’s biological father) Reggie, played by Andre Holland, and her brother (Anthony Mackie), a high-powered attorney who isn’t above playing dirty by painting Elliot as a racist in court to win Rowena full custody of Eloise.

“Black or White” gradually offers a lurid mystery regarding just how bad Reggie is, as when he attempts to extort $25,000 from Elliot in exchange for endorsing the latter as the rightful guardian in court. But discovering those new depths make for a disheartening experience, especially since the character (and his complicated relationship with his mother) eventually suggests 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, even if all the children play in an adorable but improbable jazz ensemble.

A rousing and fair debate between the little girl’s white grandfather and black grandmother would have lent the film some badly needed dramatic urgency. But “Black or White” takes a side — that of the beleaguered white man — a narrative choice that becomes all the more frustrating when Elliot’s speeches in court are portrayed as impassioned or wryly clever. (Costner gets one rather moving and ambitious monologue about overcoming racism as a continual process, not a terminal endpoint.)

Rowena’s attempts to express herself, on the other hand, are presented only as inappropriate outbursts. Nor is Rowena ever afforded the opportunity to expound her most compelling reasons for seeking Eloise’s guardianship, which are briefly mentioned at the film’s beginning, then never referenced again. By the film’s end, the “Black or White” raises only one question: Is its racial-baiting disingenuous or oblivious?