NFL commissioner Roger Goodell. (Paul Beaty/AP)

Whatever you think of Roger Goodell, commissioner of the National Football League, you should recognize that he’s trying to solve a genuinely hard problem. Or rather two problems. On one hand, he’s trying to maximize the audience for NFL games. At the same time, he’s also trying to negotiate the same fraught racial politics that our nation has been struggling with for centuries, but in miniature, and in prime time.

Nearly 70 percent of NFL players are black. Why wouldn’t those players want to use their privileged position to highlight one of the most pressing problems facing their community today? But the last time the Nielsen Year in Sports report broke down the numbers, in 2013, football’s viewership was 15 percent black but 77 percent white. Only 35 percent of whites are sympathetic to the Black Lives Matter movement, which seems a reasonable proxy for their sympathy for the kind of in-your-face protest that refusing to stand for the national anthem represents.

Let’s be clear: Whites should be more sympathetic to the problem of racial inequities in the criminal justice system. If cops treated whites the way they treat blacks, white people would not be arguing that crime is a real problem, and that profiling is just statistics; they’d be frantically calling their legislators and muttering about the Second Amendment.

But few human beings of any color are as keenly alive to the suffering of others as they are to their own travails. So however desirable, it seems unlikely that white America en masse will suddenly muster towering outrage about a problem that doesn’t much affect them. Not even if they see athletes protesting it on national television.

Which leaves Goodell with a problem. Some sizable fraction of his audience views American criminal justice overreach as less worrying than disruptive protests of same. They get very angry when football players hijack their leisure viewing to deliver an unwelcome political message. And even some who believe that police brutality is a large problem are made uneasy when protesting it involves refusing to honor a symbol of American national unity.

Meanwhile NFL viewership is down 17 percent since 2015. Attendance and public perception about the NFL are also hurting. There’s a robust debate over whether the protests are contributing to the decline, but we’ll sidestep that, since I know little about the sport, and the opinions of people who do know something largely seem to be conveniently correlated with their opinions about the protesting players.

Suffice it to say that football is facing a lot of problems, all at once. Cord-cutters. A glut of football games that makes them less rare and special, and therefore, one less thing that millions of Americans still watch together. A CTE crisis that is cutting into youth play (and eventually into future viewership) and makes many adults queasy about watching healthy young men systematically destroy each other’s brains.

The decline of football may simply be inevitable. But even so, it’s probably a bit much to expect an NFL commissioner to say “I guess we’re doomed” and seek meaning in the impending death by sending the league on a suicide charge against racial inequality.

The solution that the league’s owners actually chose was the kind of mushy compromise America used to specialize in, designed to please no one but satisfy everyone. Teams will be fined if their players kneel during the anthem, but players are allowed to stay in the locker room if they don’t want to stand. Except the America where that type of agreement once worked no longer seems to exist; the new rule has merely fanned fresh outrage. The left complained about billionaires suppressing free speech and punishing dissenters and threatening players into showing respect. President Trump, meanwhile, said: “You have to stand proudly for the national anthem or you shouldn’t be playing.”

Which encapsulates another problem that this country is struggling to solve: the burgeoning politicization of every facet of American life. And not just the vague patriotism of playing the national anthem at sporting events, but the specific political vision of one of our nation’s two warring tribes.

There has always been some of this, of course; the last time American public spaces were truly apolitical was probably sometime before the Clovis People arrived 13,000 years ago. But by and large, high-profile public entities like sports leagues and major corporations have stayed firmly in the bland center. Now, however, it’s getting harder to resist the centrifugal forces tugging them outward.

Of course, when you’re fighting for an important cause — and what cause is more important than seeing every citizen treated equally by our police and our courts? — then it seems outrageous to suggest that something so venal as NFL finances, so banal as enjoying a Sunday afternoon football game, should take precedence over your concerns.

The practical objection to that retort is that if NFL revenue collapses, its players will no longer have such a prominent forum from which to mount their protest. Indeed, many fans will blame them for the decline of their favorite sport, which is unlikely to make them feel more warmth toward the cause of criminal justice reform.

But there’s a deeper, and arguably more important, objection: A healthy society needs to foster spaces where we forget about our political divisions and unite over something else. Without those spaces, we won’t have the common reservoir of goodwill, of shared identity, from which durable political change must ultimately be forged.

Of course, creating those spaces raises the specter of what David French has called “corporate censorship … every bit as oppressive as the campus or corporate attacks on expression that conservatives rightly decry.” And we should indeed be keenly alive to that danger.

But we also do have to recognize that there are limits to what we can expect companies to do in the name of free speech. We should broadly tolerate people whose opinions differ sharply from our own, and we should make allowances for those differences in the workplace as often as possible. We certainly shouldn’t go prying into the off-hours activities of employees unless they pose a clear and obvious threat to business operations. But those principles are weaker when it comes to what people do when they’re on the clock. If a Williamsburg grocery clerk insists on sharing the Good News about Jesus Christ with outraged customers while ringing up their milk and eggs, I doubt many of the people currently waxing lyrical about corporate censorship would argue that the owners are obligated, as a matter of liberal principle, to allow this state of affairs to continue.

That may seem a bit rich, coming from someone who gets paid to opinionate for a living. But spaces that are dedicated to the free exchange of ideas have a different mission from places that are dedicated to selling groceries or playing football. I am not concerned that The Post does a poor job of providing me an excellent range of farm-fresh produce; I would be concerned if we stopped trying to bring our readers a diverse array of information and analysis. And when it comes to that grocer, those priorities are reversed.

Companies should support free speech wherever possible, but not to the extent of compromising their other missions. And the central mission of some places includes giving us a space where we don’t have to think about politics. Most people don’t want to immerse ourselves in politics 24/7; in fact, most people can’t stand it. Forcing us to live that life doesn’t turn us into agents of social change; it makes us angry and frustrated, and less willing to come together with our opponents to actually change anything.  Except maybe the volume knob on the screaming, as our current politics illustrates so well.

Fervently supporting free speech doesn’t necessarily imply that everyone should have to listen to that speech every waking moment. Which is why you can support what the athletes are kneeling for, and their right to speak forcefully for their opinions without retaliation or censure — and yet still recognize the wisdom of a Goodell-style compromise that leaves Americans at least a few arenas where they only have to root for one team at a time.

Read more:

Karen Attiah: It’s time to cancel the NFL and its plantation-style politics

Elizabeth Bruenig: All Colin Kaepernick ever did was ask

The Post’s View: Sterling Brown’s arrest shows why NFL players have a reason to kneel