If there’s one thing Washington’s establishment can do fairly well, it’s trade backbiting for black tie — if only for one night. And Saturday’s Alfalfa Club dinner, that annual meeting of the millionaires, provided a good example of that.

Not familiar with the fancy affair? Every year, the exclusive society of chief executives, politicos and philanthropists gathers for one purpose — to drink and hobnob in the nation’s capital. That’s it.

There’s no other purpose to the century-old club besides this one heavy-hitting banquet featuring funny speeches aimed at the wealthy targets in the Capital Hilton ballroom, where the seating chart reads like a yearbook for the 1 percent.

Microsoft’s Bill Gates, former New York City mayor Michael Bloomberg (the club’s new president), super investor Warren Buffett, Oracle’s Larry Ellison and Amazon’s Jeffrey P. Bezos (who also owns The Washington Post and the priciest residential property in town) were scheduled to attend.

“Of the eight richest men in the world,” said our source at the dinner, which is closed to the media, “I think five of them were in the room.”

Well, those guys and Kellyanne Conway, counselor to President Trump.

That’s the one thing that was markedly different about Saturday’s dinner — Washington has in fact changed a bit. The “establishment” now includes a reality star turned president who, just one day before the annual dinner, signed an executive order on refugees and others seeking to enter the United States that set off a weekend filled with protests.

Is it politically correct (or even good optics) to be yukking it up in a tuxedo when people are showing up at airports in support of detained travelers from New York to Texas? The Alfalfans seemed to think so.

Outgoing club president Erskine Bowles, a former White House chief of staff during the Clinton administration, lobbed punchlines at Vice President Pence (“As a special treat, sir, we have arranged for the cast of ‘Hamilton’ to perform for you”) and Trump’s penchant for flouting precedent (“You know those turkeys that previous presidents pardoned every year? President Trump plans to eat ’em.”).

Vernon Jordan’s task was to read the “crop report,” a.k.a. the list of the club’s newest inductees or “sprouts,” which this year included Mary Barra, CEO of General Motors; Brendan Bechtel, CEO of the Bechtel Group; Sen. Amy Klobuchar (D-Minn.); Sen. Charles E. Schumer (D-N.Y.); and Dina Powell, a former Goldman Sachs executive who now serves as an assistant to the president.

Jordan, a former adviser to President Bill Clinton, joked that with so many Goldman Sachs execs headed to 1600 Penn., “Hillary Clinton won’t have anyone to give speeches to.”

Former defense secretary Robert Gates served as the club’s faux nominee for president of the United States. Gates joked that if elected he’d also appoint Ben Carson, who was in the room, to his Cabinet.

“He’s one of the world’s great brain surgeons,” Gates said, “but he gave it up for politics. I guess he wanted to get as far away from brains as he could.” Ba dum bum.

Gates also gave a shout-out to Ivanka Trump, the president’s elder daughter, and said he’d appoint her husband, Jared Kushner, as his son-in-law. The young couple were in the room along with fellow Trump insiders, White House press secretary Sean Spicer, White House chief of staff Reince Priebus and Conway. The trio of staffers were all seated at the head table. (White House senior counselor Stephen K. Bannon skipped the dinner at the last minute.)

The boss himself was a no-show, despite the noticeably heightened security around the hotel that had prompted some attendees to assume that Trump had changed his mind and would follow tradition and make a surprise appearance. No such luck.

In his stead, Pence delivered the night’s closing remarks, which included a timely (and perhaps ill-timed) nod to the border wall. The vice president said the administration planned to build a wall between the White House and the press — and that the New York Times was going to pay for it. That line apparently got huge laughs.

What cut deepest, however, was the message in between the punchlines.

Before handing over the mic to Bloomberg, the incoming club president, Bowles said that what he loved about Alfalfa was club members’ ability to spend a jovial bipartisan night together in an increasingly fractured town.

“And in doing so, we can build the bonds needed to bring the country together and to solve some of the problems facing us today,” added Bowles, who then addressed Ivanka Trump directly.

“Ivanka, please tell your dad that we missed him tonight, and we wish him, as the leader of our country, a healthy and successful presidency.”

Our mole in the room said that same sentiment permeated the rest of the evening. Another person who attended the after-party held at Cafe Milano in Georgetown said Trump’s nominee for secretary of state, Rex Tillerson, was surrounded on all sides, like a “grown-up” life raft. Former secretary of state John F. Kerry was there too. There was no word on whether the pair ever found a quiet corner to trade notes. But we’re told the word “hopeful” kept coming up in conversations.

“You heard it all over,” said our tipster in the ballroom, “as if people were trying to convince themselves.”