By Kevin Liptak and Jeff Zeleny, CNN

(CNN) -- In the cavernous sanctuary of the National Cathedral on Wednesday, President Donald Trump came face-to-face for the first time with his four living predecessors, an encounter occasioned only by a loss to the most exclusive club in American politics -- indeed, in the world.

Trump's election, which came after he demeaned and humiliated the family members of three ex-presidents and made racist insinuations about his predecessor, has shaken the traditional fraternity of past and current commanders in chief. He had, until now, avoided any encounters with the collected group, and hadn't spoken at all with three of them. He has neither consulted them on issues nor avoided overt criticism of their presidencies, breaking tradition on matters large and small.

For the time he is inside the cathedral on Wednesday morning, those hurtful slights are likely to remain unmentioned. But few believe the death of President George H.W. Bush will lead to new camaraderie between Trump and the men who served before him.

As he was shown to his seat, Trump reached over his wife to shake President Barack Obama's hand, who greeted him with a nod. It was their first interaction since Inauguration Day almost two years ago.

Michelle Obama offered Trump a quick "good morning" before looking forward. Trump did not shake hands with the Clintons or the Carters, seated several seats away, though first lady Melania Trump extended a hand to greet President Bill Clinton, who smiled warmly.

The nation honors President George H.W. Bush: Live updates

The presidents club, by nature, is complicated by past rivalries and future legacies. Yet regardless of party, the members -- so far, all men -- are bound by their singular experience of serving in the Oval Office. It's impossible to know, at this stage of his presidency, what Trump's ultimate role in the club will be. But he enters the group carrying a long record of dismissive, vitriolic criticism extending well beyond partisan politics.

Club of competitors

The late President Bush was himself a testament to the bygones-be-bygones nature of a club that is composed of political competitors. After Bush's bruising loss to Clinton in 1992, the two men eventually teamed up to lead humanitarian efforts after a devastating tsunami in Asia.

Trump, who maintains grudges going back decades, has shown little interest in developing relationships with his predecessors during his first two years in office, according to those who have spoken with him. He has reached out to them sparingly, including a birthday phone call to the elder Bush two summers ago. When Trump selected Brett Kavanaugh as his Supreme Court nominee in July, he placed a call to George W. Bush, whom Kavanaugh had served in the West Wing as staff secretary. Later, the younger Bush phoned lawmakers to press for Kavanaugh's confirmation.

But until Wednesday, Trump has not spoken to Obama since they parted ways at the East Front of the US Capitol two Januaries ago, where the new President waved off the last as Obama left Washington in a military helicopter. If protocol abides, the two men will be separated by only one seat at the cathedral, filled by first lady Melania Trump.

Neither has he spoken to Clinton or his 2016 rival, Hillary Clinton, who will be seated a few feet away at Wednesday's service. And he hasn't phoned President Jimmy Carter, though did take notice when the former president suggested the media don't treat Trump fairly, and Trump praised the Democrat in private to his friends.

That's a break from how presidents have usually interacted with the men who've held the job in the past. Acrimony, even after fiercely contested elections, is usually cast aside or at least aired only in private. Most presidents occasionally consult in some capacity with one or more of their predecessors, usually in private.

Bush family and Trump

The tensions between the Bush family and Trump, which were a recurring theme of the 2016 Republican primary after Trump belittled GOP rival Jeb Bush, roared back into public view after Barbara Bush died in April. She had been highly critical of Trump, saying at one point: "He's said terrible things about women, terrible things about the military. I don't understand why people are for him."

And she made clear she did not want him at her funeral.

But shortly after her body was laid to rest, when it seemed as though her husband's health was failing and his death was imminent, the Bush family reached out to the White House to inform Trump the state funeral for Bush would be different. The former president wanted the current occupant of the office to attend, two people familiar with the conversations said.

It was less of an olive branch than a sign of the former president's penchant for protocol, a Bush family friend said. The decision also meant that the week of Bush's death would be devoted to a celebration of his life and service, not a messy public feud with Trump.

"This is a chance for the country to remember -- and learn again -- about 41," a Bush family friend said.

Trump, who campaigned as an outsider and has grown accustomed to not being welcomed into several elite clubs and social circles in New York, has indicated that he appreciates the gesture.

"The elegance and precision of the last two days have been remarkable!" Trump tweeted.

He has maintained a gracious and reverent demeanor this week, including traveling late Monday to view Bush's casket lying in state in the Capitol Rotunda and paying a call to Blair House, where the Bush family is staying, on Tuesday. Former first lady Laura Bush and Melania Trump, who have maintained warmer ties than their husbands, toured the White House Christmas decorations.

"In this case, I think that it is important to show the continuity between presidents, that Donald Trump isn't just an individual, he represents the institution of the presidency, which 41 held so dear," said Douglas Brinkley, a CNN presidential historian and professor at Rice University.

"So it's very appropriate that he's there. My concern is strange tweets in the middle of it, because of all the Mueller investigation things coming out. He very well may be behaved during the ceremony and 15 minutes later be writing strange things," Brinkley added.

Harsh words

Only five months ago, the President was mocking Bush's trademark "thousand points of light" philosophy of public service during a rally in Montana.

"What the hell is that?" Trump asked supporters in July. "Has anyone ever figured that one out? And it was put out by a Republican, wasn't it? I know one thing: Make America Great Again we understand."

He has bluntly said George W. Bush "lied" about the Iraq War -- hardly a controversial sentiment among many Democrats, which Trump was for much of his life -- but he took it a step further while campaigning in 2016.

"Excuse me, the World Trade Center," Trump said, a pointed reference to how the September 11, 2001, terrorist attacks took place on Bush's watch. Since taking office, Trump has privately derided the younger Bush as "genius" for entering the Iraq War.

Trump's most incendiary comments of all come through his inaccurate and racist questioning of Obama's American citizenship. In her bestselling memoir this year, Michelle Obama wrote that the birther conspiracy had made her worry for her daughters' safety (the former first lady canceled book tour events in Europe this week to attend Bush's funeral).

In a 2011 interview with The New York Times' Maureen Dowd, George H.W. Bush summed up his view of Trump like this: "He's an ass."

Still, the presidents club is like family -- members have little say in who joins.

Indeed, the club runs more on tradition and the forging of personal relationships than on etched rules or guidelines. It's an exclusive gathering that primarily convenes to christen a presidential library or to bid farewell at a state funeral, though George W. Bush made a point of inviting all the former presidents, including his father, to meet Obama as he was entering office in 2009.

The services for Bush on Wednesday will be the fourth state funeral at the soaring National Cathedral in Washington, with Gerald Ford's in 2007, Ronald Reagan's in 2004 and Dwight D. Eisenhower's in 1969.

Bush "planned his funeral memorial service right to have President Trump attend. But let's be honest -- there's nobody that wants to see President Trump at this memorial service that's going to be there," Brinkley said. "But he's going to be there. And what's going to be interesting -- people will be looking to see who comes up to him, how does everybody act."

"People will have to endure the fact that President Trump is there," Brinkley said. "But it's good that he's there."