Relativity’s “Black or White” is fighting an uphill battle for attention as the crowded awards race heats up, which is a shame since it’s one of the most timely films of 2014.

Like some other late-year entries (“The Gambler,” “Six Dance Lessons in Six Weeks,” etc.), the film is concentrating its awards hope on performances and script. “Black or White” qualifies in both categories. It also carries a sense of immediacy. No matter who you think is right in Ferguson, Mo., this past week’s events prove that race relations in this country are a mess.

Hollywood movies have addressed bigotry for many decades, and the message is inevitably “Can’t we all just get along?” At this point, it’s hard to add something new to the conversation, but writer-director Mike Binder raises points of view that are rarely depicted.

Kevin Costner is great as a prosperous L.A. man in a custody battle with a woman (supporting actress Octavia Spencer) over their biracial granddaughter. Both want what’s best for the girl and insist that race has nothing to do with it. But they slowly realize that prejudices, on every side, are more ingrained than they’d like to admit.

Binder brought the script to Costner, who not only agreed to star, but to put his own money into the production after the major studios passed. So you can’t help rooting for the film. It’s by no means perfect, but it’s entertaining and well made. In any other year, Costner would be a shoo-in for a best actor Oscar nomination.

Awards buzz is always self-fulfilling: The more people talk about a film, the more others talk about it. So the lack of attention from pundits and the Indie Spirits doesn’t hurt “Black or White,” but it doesn’t help it either.

The film is also in danger of being overshadowed by “Selma,” as if the awards season only has room for one movie about race relations. This year marks the 50th anniversary of the Civil Rights Act. That’s a long time — two generations — so racial equality should logically be second nature to all of us by now.

Unfortunately, real life is rarely logical, so these two films (and others with similar themes) are sadly relevant.