Archive is background info via this BBC post from 2023, but that's just one piece. Yeah, a lot of us have seen the photo, and maybe some of us know it was during the Viet Nam War, during Civil Rights protests in the U.S. and not that long after the assassination of MLK. Maybe you even know that Muhammad Ali lost his belt and was banned from boxing in the U.S. for refusing the draft to Viet Nam:

"Why should they ask me to put on a uniform and go ten thousand miles from home and drop bombs and bullets on brown people in Vietnam while so-called Negro people in Louisville are treated like dogs and denied simple human rights?"

I did not know the Black Power Salute got all 3 athletes BANNED from the Olympics and pretty much ruined their lives. From NPR post for 50th anniversary:

Both men received hate mail and death threats. There was discussion of stripping them of their medals. Many Americans shunned them for their silent gesture: For years, they struggled to find good jobs. Their marriages suffered under that strain. Their children were bullied at school. Employers shied away from them.

And Smith and Carlos were banned from future participation in any Olympics for life. (They were in their early 20s in Mexico City, and this effectively prevented them from competing in other races in Munich and Montreal.) There were no offers of the complimentary stadium tickets usually offered to medaled athletes.

(Peter Norman suffered many of the same indignities when he returned to Australia. He was ostracized, never allowed on an Australian Olympic team again, despite qualifying in several national trials.[...]

Which gets us to The White Man In That Photo (from 2015 -- long and worthy of a full read):

Norman was a white man from Australia, a country that had strict apartheid laws, almost as strict as South Africa. There was tension and protests in the streets of Australia following heavy restrictions on non-white immigration and discriminatory laws against aboriginal people, some of which consisted of forced adoptions of native children to white families.

The two Americans had asked Norman if he believed in human rights. Norman said he did. They asked him if he believed in God, and he, who had been in the Salvation Army, said he believed strongly in God. “We knew that what we were going to do was far greater than any athletic feat, and he said “I’ll stand with you” – remembers John Carlos – “I expected to see fear in Norman’s eyes, but instead we saw love.”

Smith and Carlos had decided to get up on the stadium wearing the Olympic Project for Human Rights badge, a movement of athletes in support of the battle for equality.

They would receive their medals barefoot, representing the poverty facing people of color. They would wear the famous black gloves, a symbol of the Black Panthers’ cause. But before going up on the podium they realized they only had one pair of black gloves. “Take one each”, Norman suggested. Smith and Carlos took his advice.

But then Norman did something else. “I believe in what you believe. Do you have another one of those for me”? he asked, pointing to the Olympic Project for Human Rights badge on the others’ chests. “That way I can show my support for your cause.” Smith admitted to being astonished, ruminating: “Who is this white Australian guy? He won his silver medal, can’t he just take it and that be enough!”.

So they all go to the podium in solidarity and the U.S. winners give the salute and suffer the aftermath. More from 'white guy':

As John Carlos said, “If we were getting beat up, Peter was facing an entire country and suffering alone.” For years Norman had only one chance to save himself: he was invited to condemn his co-athletes, John Carlos and Tommie Smith’s gesture in exchange for a pardon from the system that ostracized him.

A pardon that would have allowed him to find a stable job through the Australian Olympic Committee and be part of the organization of the 2000 Sydney Olympic Games. Norman never gave in and never condemned the choice of the two Americans.

He was the greatest Australian sprinter in history and the holder of the 200 meter record, yet he wasn’t even invited to the Olympics in Sydney. It was the American Olympic Committee, that once they learned of this news asked him to join their group and invited him to Olympic champion Michael Johnson’s birthday party, for whom Peter Norman was a role model and a hero.

Norman died suddenly from a heart attack in 2006, without his country ever having apologized for their treatment of him. At his funeral Tommie Smith and John Carlos, Norman’s friends since that moment in 1968, were his pallbearers, sending him off as a hero.

Note that the 'white guy' article talks about a commemorative statue built in 2005 of just Smith and Carlos -- no Norman. Norman approved that artistic choice. Transcript from Democracy Now where Carlos himself explains how he called Norman to hear him say so (part 1 and part 2):

JOHN CARLOS: Yeah, “Blimey, John. You’re calling me with these blimey questions here?” And I said to him, I said, “Pete, I have a concern, man. What’s this about you don’t want to have your statue there? What, are you backing away from me? Are you ashamed of us?” And he laughed, and he said, “No, John.” He said—you know, the deep thing is, he said, “Man, I didn’t do what you guys did.” He said, “But I was there in heart and soul to support what you did. I feel it’s only fair that you guys go on and have your statues built there, and I would like to have a blank spot there and have a commemorative plaque stating that I was in that spot. But anyone that comes thereafter from around the world and going to San Jose State that support the movement, what you guys had in ’68, they could stand in my spot and take the picture.”

The U.S. (but not just the U.S.) has a woeful history of treating those who protest Injustice horribly. There's always an excuse for it, too. From the above articles, we can see that the Olympic head allowed the Nazi salute for the ~~Munich~~ Berlin games but expelled Smith and Carlos in 1968 with the rational that the first was a national salute and therefore acceptable whereas 'Black Power' was not.

More recently, Kaepernick kneeling got him in trouble with the NFL but they were fine with Butker's speech that, "denounced abortion rights, Pride Month, COVID-19 lockdowns..." and suggested women should be homemakers instead of using their newly earned college diplomas. Supposedly the 'difference' is that Kaepernick's silent protest was on the NFL's time but Butker spoke on his own time so it was fine ... but they can always find a difference and it is never as valid as simply siding against injustice.

EDIT: I inadvertently typed 'Munich' instead of the correct 'Berlin' games for when the Nazi salute was allowed. Fixed now.