Patriots quarterback Tom Brady smiles and waves goodbye to the media after being asked by a reporter about his supposed friendship with Republican presidential hopeful Donald Trump at the NFL football team's facility. (Stephan Savoia/AP)

Tom Brady has a Malcolm X problem.

Not that Malcolm X was, or is, a problem to me. But in the early 1960s, when rumors swirled that the Muslim minister was counseling a young Olympic boxing gold medalist who was contending for the heavyweight boxing championship, Malcolm X was a frightening figure for much of America.

Indeed, in 1959 Malcolm X was a central figure featured in a week-long New York television documentary narrated by Mike Wallace titled “The Hate That Hate Produced.” That hate that was produced, Wallace told his audience, was a black religious organization that called itself the Nation of Islam. Wallace described the Nation as “the most powerful of the black supremacist groups.” Wallace’s reporting cohort on the show, Louis Lomax, interviewed Malcolm X about the Nation’s view of white Americans. Malcolm X responded: “By nature, he is evil.” He ventured further and said Nation of Islam children were taught that the white man is the devil.

The transcript became part of notorious FBI director J. Edgar Hoover’s surveillance files of the Nation and Malcolm X, which Hoover sought to, at the very least, disrupt. After all, Malcolm X was becoming the face and voice of a burgeoning militant black nationalist movement in America’s biggest cities.

In this Sept. 27, 2015, file photo, a New England Patriots fan holds a sign that refers to Patriots quarterback Tom Brady and Republican presidential candidate, businessman Donald Trump during a game between the Patriots and Jacksonville. (Charles Krupa/AP)

So on the morning of Feb. 26, 1964, after the 22-year-old Olympic gold medalist named Cassius Clay beat Sonny Liston in a stunning upset for the world heavyweight boxing championship, a reporter at a news conference asked Clay whether it was true that he was “a card-carrying member of the Black Muslims.”

David Remnick, editor of the New Yorker and former reporter at The Washington Post, recalled the moment in his Muhammad Ali biography, “King Of The World”:

“Clay recoiled not so much from the idea of breaking news — he had assumed by now that everyone knew he was a convert to the Nation of Islam — but rather from the terminology. ‘Card-carrying’ had the ring of McCarthyism, and ‘Black Muslim’ was a term repugnant to members of the Nation. ‘Card-carrying: What does that mean?’ ” Clay said. “ ‘I believe in Allah and in peace. I don’t try to move into white neighborhoods. I don’t want to marry a white woman. I was baptized when I was 12, but I didn’t know what I was doing. I’m not a Christian any more. I know where I’m going and I know the truth, and I don’t have to be what you want me to be. I’m free to be what I want.’ ”

Brady, the Patriots’ champion quarterback, shirked to explain his association with Republican presidential front-runner Donald Trump when questioned Wednesday by a New York Daily News reporter. That was Brady’s right.

What was most disturbing, however, was that people in my vocation questioned the reporter asking the question. As a journalist, that was his obligation.

Trump isn’t just one of two leading candidates at this moment to win the most powerful government seat in the world next November. He is the subject of great debate for what he has said and what he has proposed to do if elected president of the United States.

Last summer, Trump said he wanted to build a wall at the Mexico-U.S. border to stop Mexicans from entering the U.S. illegally because, he charged, they are rapists and criminals. Univision, the most-watched Spanish-language network in the United States, responded by dropping its broadcast of the Miss USA pageant, which at the time was partly owned by Trump.

Last month, Trump told Fox News that a black protester at his campaign rally in Birmingham, Ala., who was assaulted by a half-dozen white campaign supporters, “maybe . . . should have been roughed up because it was absolutely disgusting what he was doing.”

Earlier this month, Trump called for a temporary ban on Muslims entering the U.S. until the government can “figure out what is going on” in the wake of the Paris attacks. He coupled that with a suggestion for a national registry of some sort for Muslims, which echoed the internment of Japanese Americans here during World War II and Nazis forcing Jews to wear badges identifying their religion.

It all brought even fellow Republicans, such as operative Max Boot, a fellow at the Council on Foreign Relations who is advising Trump rival Marco Rubio, to proclaim: “Trump is a fascist. And that’s not a term I use loosely or often. But he’s earned it.”

Yet, somehow, along the way, Trump earned Brady’s friendship, respect and — by virtue of a red ballcap emblazoned with Trump’s “Make America Great Again” slogan prominently displayed in his cubbyhole — endorsement.

Why? That isn’t just a fair question for Brady but a necessary one. We sportswriters haven’t let peccadillos stop us before.

When Washington wide receiver DeSean Jackson was unceremoniously cut from Philadelphia two offseasons ago after a story suggested he affiliated with gang members, reporters interrogated him. Jackson didn’t hide. He explained, and others vouched, that the gang members he knew were peers from the neighborhood in which he was reared. He didn’t gravitate toward them as an adult as Brady has to Trump, a man Brady didn’t grow up next to and is 31 years his elder.

As the Clay-turned-Ali story reminded, Brady isn’t the first star athlete to allude to a political statement that generates wonderment. A few years ago, NBA all-stars Dwyane Wade, LeBron James and their Miami Heat teammates were photographed in black hoodies in protest of the killing of unarmed black teen Trayvon Martin. They answered questions about it.

In the run-up to the Iraq War in 2003, Steve Nash sported an anti-war shirt to an all-star game news conference. He answered questions about it.

Heisman Trophy winner Tim Tebow turned his eye-black tape into blackboards for conservative Christian messages. He answered questions about his practice, which eventually was outlawed by the NCAA.

NHL all-star and onetime Capitals wing Jaromir Jagr wears the No. 68 for a reason: to commemorate the Prague Spring in his native Czechoslovakia in 1968. He has never shied from talking about it.

Just because they are athletes doesn’t mean we in the media should dumb them down to a lowest denominator and ignore some of what we see. That’s as much an abdication of our responsibility as an athlete’s refusal to answer such an inquiry is an indication of his or her trepidation.

Kevin B. Blackistone, ESPN panelist and visiting professor at the Philip Merrill College of Journalism at the University of Maryland, writes sports commentary for The Post.