Jeff Nichols’ segregation-era drama, “Loving,” is based on the true story of an interracial couple from Virginia whose legal battle to stay married ended in victory at the Supreme Court. Although the battle for same-sex marriage ended the very same way a few years ago, the film has a subtle new relevance in the wake of a furious and fractious election season. “Loving” is a plea for tolerance, as expected, but it also suggests that America isn’t as neatly or simply divided as we sometimes think.

Writer-director Nichols (“Midnight Special,” “Mud”) builds his film upon two fine performances, from Joel Edgerton as the taciturn Richard Loving, who is white, and a sublime Ruth Negga as Mildred Jeter, who is black. They say little, communicating together mostly with their eyes and bodies. Their romance unfolds non-traditionally: first comes love, then a baby, then marriage. That requires a drive to nearby Washington, D.C., where miscegenation is legal.

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If there’s a third lead character here, it’s the Lovings’ hometown of Central Point. It isn’t a simple battleground divided between bigots and victims, but an enclave of tolerance where blacks and whites mix freely (more or less). Nobody ever addresses the topic — the less said the better, perhaps — and yet somebody rats out the married Lovings, leading to their arrest. (The film does have one stock villain, a contemptuous cop played by Marton Czokas.) Richard’s black friends have only so much sympathy — “Now you know what it’s like,” says one — and even Richard’s colorblind mother (Sharon Blackwood) frowns on her son’s behavior. The Lovings have rocked a boat that upsets everyone.

As the Lovings wage their legal war, they greet outsiders with suspicion. Nick Kroll plays Bernard Cohen, their ACLU attorney, who seems driven by ambition as much as principle. A Life magazine photographer, Grey Villet (Michael Shannon), seems slightly slick and schmoozy, but his intimate portrait of the couple — watching television, his head in her lap — turns the Lovings into a national headline.

This quiet, understated film makes its case without grand speeches or impassioned rhetoric. That’s a refreshing change from most issues-based movies, and a welcome approach at this particular moment in time.