Good news about “Invictus”: Just because it’s set in the southernmost reaches of what sometimes still is very disturbingly called “the dark continent,” and it involves political events of two decades ago (metaphorically explained by way of a locally little-known sport), and it draws its title from a relatively obscure Victorian poem with a dead-language title, doesn’t mean the film will be in any way abstruse, challenging, thematically indigestible or otherwise unsafe for consumption by formula-habituated mainstream audiences.

It was directed by Clint Eastwood, after all. And it stars Morgan Freeman and Matt Damon — who, for a true story of a human-rights hero and a rugby player, probably are the most obvious casting choices in the world. Just try not to think of “Invictus” as cultural colonialism, and everything will be fine.

“Unconquerable” is what that title means, as in “Out of the night that covers me, / Black as the Pit from pole to pole, / I thank whatever gods may be / For my unconquerable soul.” Written in 1875 by the British poet William Ernest Henley, those lines, and the dozen others that follow, supplied Nelson Mandela with words to live by during the 27 years of prison captivity he endured until 1990, when “Invictus” begins.

“It is that terrorist Mandela — they let him out,” says a wolfish rugby coach to his over-starched white team in the movie’s first few minutes. “Remember this day, boys. This is the day our country went to the dogs.” But of course the poor black kids playing soccer behind a fence across the street don’t see it that way at all. And then, with a few quick strokes of Freeman-infused historical montage, and a few tranquil trumpet notes of Kyle Eastwood’s typically anesthetic score, the post-Apartheid era, and the Mandela presidency, has begun.

“He can win an election, but can he run a country?” Freeman’s carefully calibrated accent asks, reading a newspaper headline, and adds: “It’s a legitimate question.” Lest this moment seem too politically intricate for American audiences, Eastwood promptly neutralizes it: Imagine an old Reagan campaign commercial dressed in drag as one for Obama. It’s morning again in the Republic of South Africa. We actually see the sun coming up over shanties. We also see Matt Damon as Francois Pienaar, in a “South Africa Rugby” T-shirt, watching Mandela’s ascendance on TV with interest, and absorbing his own father’s reactionary insecurities with a tellingly level head.

Notwithstanding the protracted ministrations of establishing his half black, half-Afrikaner security detail, it isn’t long before the president has invited the rugby captain to tea, reminded him, with help from Henley’s poem, to be the captain also of his own soul, and told him, “In order to build our nation, we must all exceed our expectations.” Imagine a social-issue movie dressed in drag as an inspirational-underdog sports movie….

Thing is, it all actually happened. However close the film pushes to preposterousness (very), however many post-racial platitudes it regurgitates (many), there’s no denying Mandela’s real insight that the malleable symbology of the Springboks rugby team might actually offer his riven nation a way toward its better future. “Under the bludgeonings of chance,” Henley wrote, “my head is bloody, but unbowed.” Surely if a black man can keep those words in his mind while doing decades worth of hard time, a white man can take them to heart on a playing field during the game of his career. And surely the rest of us can be moved by their common efforts.

Anthony Peckham’s screenplay (adapted from John Carlin’s book, “Playing the Enemy”) gets nudgy and redundant, and Eastwood, not even minding his own artlessness as usual, follows suit. “Invictus” never quite makes us understand what life during and since Apartheid really is like. Maybe that’s not the point, but it shouldn’t be negligible either. The film abbreviates Mandela’s other affairs of state, and his estrangement from his family, to make room for mantra-like reiterations of its own rousing theme. But the resonant essence of the story, and its stars’ apparently infinite likability, go plenty far on their own.

Morgan Freeman and Visa hope to see you at the Olympics, but if you can’t make it, maybe “Invictus” will do.