For a long time, if you said the name “the Reverend Al Sharpton,” you were guaranteed to get a response that seemed to erupt from the very gut fauna of mass-media outrage. “Loudmouth,” the fascinating new documentary about Sharpton, makes a convincing case that most of that moral high dudgeon was fatally overblown. In the ’80s and ’90s, Sharpton was at the molten center of every race-based news event in the greater New York area. Some would say, quite reasonably, that this made him a devoted activist. (No one ever pilloried the Rev. Martin Luther King Jr. for showing up too much.) At rallies, at protest marches, on the courthouse steps, Sharpton spoke with a prickly ferocity and power, giving voice to those who didn’t have it.

Was he a new version of King or Gandhi? Of course not. And he didn’t need to be. He was his own creation — the Civil Rights agitator in a track suit who bridged the activist idealism of the ’60s with something ruder, more brazen, and (in hindsight) completely necessary: the showboat tactics of the contemporary media age. With his pouffy hair and mustache and a gleam that was at once doe-eyed and reptilian, he looked like Prince’s doughy brother, and a lot of people — almost all of them white commentators — viewed him with deep suspicion. Early on in “Loudmouth,” we see a clip of Lesley Stahl, on “60 Minutes,” interviewing Sharpton for a segment and suggesting, with a smirk, that there’s a clear contradiction between his activism and the fact that he lives in “a fancy place.” You listen to that and think: Really? Is that a contradiction, or is it a white double standard?

But Sharpton endured this sort of thing every day. In the documentary, there’s footage from a protest march he led in Bensonhurst, Brooklyn, to throw light on the murder of Yusef Hawkins, the teenager who was shot to death after he and his brother and two friends were attacked by a white mob. We see footage of neighborhood kids at the march grinning and shouting “White power!” into the news camera, and one young man says, “It’s all the media’s fault! These things should be kept quiet! Al Sharpton, go home!” The self-righteousness and, indeed, the virtual acknowledgement of guilt encoded in that statement are jaw-dropping. (What sort of defense is: This is an outrage! It should have been hushed up!) What we’re hearing is the voice of tribal racism.

If you really think about it, though, what that unabashedly racist kid was saying — that it’s all the media’s fault! — is a crudely direct echo of the drumbeat of criticism that Al Sharpton endured for decades as an activist. The mantra was always the same. He was called a showman, a huckster, a one-man publicity machine, a sham crusader addicted to putting himself in the spotlight. There’s no point in denying that Sharpton, as he confronted cases of racial antagonism and racial murder, most of them in the outer boroughs of New York, did all he could to draw the media spotlight to those cases. With a bullhorn in hand, he was a natural-born speaker and, yes, a ham — a preacher-orator who liked to hear himself talk.

Yet just watch “Loudmouth” and listen to his words. The film includes a lot of footage of his earliest days, when he was the youth director for the 1972 Shirley Chisholm presidential campaign (he was all of 18), or when he worked for James Brown and Operation Breadbasket, or when he protested racial murder ­— notably by police officers — using the same hard, flat commanding rhetoric he used, decades later, to talk about George Floyd and Trayvon Martin. Sharpton sought the spotlight, but what he said was never a sham. His words brought heat and light. They were disciplined. They were focused on questioning the system. Which is why the system, in many ways, tried to write him off.

“Loudmouth,” directed by Josh Alexander, is a sprawling and searching and, in some ways, undisciplined movie. At a time in America when the spotlight has been newly focused on racial injustice, the film powerfully channels the racial tumult of the 1980s, giving you heaps of eye-opening news footage of the time. Cries of “No justice, no peace!” filled the air of the protests that Sharpton organized, yet getting the establishment to actually listen and respond was a daily uphill climb. Everything in the documentary that’s set in that earlier era feels riveting and essential.

But half the movie is set in the present day, with Alexander following Sharpton around in his current role as svelte éminence grise of the racial-justice movement. Around the time he was running for the senate seat in New York, Sharpton underwent a dramatic transformation, shedding 175 pounds and toning down his incendiary surface. He became a cable-news pundit, a national icon, an elder statesman of the movement. This is all essential to show, and Sharpton, seated in the two-story wood-paneled book-lined parlor of his home, offers a fantastic deconstruction of how the media viewed him, and what the agendas driving that view were really about.

Yet the film, at two hours, still feels padded out with recent history. I would have liked, instead, to see some other dimension of Sharpton — who he is away from the protest marches. “Loudmouth” feels highly controlled, almost overly focused on Sharpton’s political identity at the expense of everything else. And there’s one place where the film makes a serious compromise, one that echoes the compromise that Sharpton himself has made.

In the ’80s and early ’90s, he brought crucial attention to cases of racial violence, and the accusations of demagoguery leveled against him, like the ones hurled by New York Mayor Ed Koch, were paranoid and unjustified. But Sharpton, after a mostly spotless track record, handed his critics a grenade to use against him when he got involved with the case of Tawana Brawley, the teenager in upstate New York who claimed that four men, including a police officer and a district attorney, had abducted and raped her. She was found in a trash bag, her hair smeared with feces, racial epithets scrawled across her belly. It looked like a hideous atrocity, and Sharpton treated it as one more incident in line with the Howard Beach murder and the Bernard Goetz subway shooting. But in this case, the facts were not there. This video report from The New York Times offers a definitive encapsulation of what really happened in the Tawana Brawley case. Simply put, she lied.

Sharpton claims, to this day, that Tawana Brawley deserved her day in court, and he’s right about that. Which is why he was right to sign on to the case. But once the realities began to come to light, he should have backed off. The Brawley case became a conspiracy theory, and the fact that Sharpton, interviewed in the present day, will not acknowledge that she lied — even though you can tell, from what he says, that he knows she did — amounts to a serious blemish on his legacy. He claims to stand for truth and justice. And he does. He should have been big enough to acknowledge his one defining mistake. If he had, it wouldn’t define him as much.

Yet one blemish doesn’t blot out the moral urgency of what Al Sharpton stands for. He took risks and paid a price, at one point getting stabbed in the chest with a kitchen knife by one of those Bensonhurst residents. In “Loudmouth,” Sharpton offers the best defense of his tactics in his eulogy for George Floyd. From a Minneapolis church podium, he declares, “Critics would say that all Al Sharpton wants is publicity. Well, that’s exactly what I want. ‘Cause nobody calls me to keep a secret. People call me to blow up issues that nobody else would deal with. I’m the blow-up man, and I don’t apologize for that.” But then he adds, with a rhetorical power that builds, “George Floyd’s story has been the story of Black folks. Because ever since 401 years ago, the reason we could never be who we wanted and dreamed of being is that you kept your knee on our neck.” Al Sharpton spent decades working to lift that knee off. If that isn’t heroism, I don’t know what is.