But after Mr. Trump entered the Oval Office, the network’s opinion hosts — from the cast of the president’s favorite morning show, “Fox & Friends,” to the anchor of “Hannity” — began to cheerlead his agenda more and more. Ratings and revenue increased, thanks to the overlap between the network’s audience and the Make America Great Again crowd.

On Monday night, though, with its biggest star joining Mr. Trump at a raucous campaign event, Fox News entered new territory — a thicket in which it’s hard to tell where the network ends and the president begins. The morning after, Fox News employees were complaining about what had happened in Cape Girardeau.

Mr. Trump introduced Mr. Hannity — an informal adviser and close confidant since the 2016 campaign — as someone who had been “with us since the beginning.” After a firm handshake and a warm bro-hug, Mr. Hannity pointed toward the reporters in the back and said, “By the way, all those people in the back are fake news.”

The host and the president smiled as the crowd jeered the press pen — which included the Fox News White House correspondent Kristin Fisher. Then Mr. Hannity delivered, in a thunderous voice, one of the Trump campaign’s slogans: “Promises made, promises kept!”

His Fox News colleague Jeanine Pirro also appeared on the rally stage that night. “Do you like the fact that this man is the tip of the spear that goes out there every day and fights for us?” she said, to cheers.

.. For all his many faults, Mr. Ailes understood the value of maintaining at least the semblance of separation between the network and the political party he was effectively commandeering from his desk in Manhattan. And he believed he had to protect his stable of news correspondents and producers to give Fox News some credibility beyond the core viewers who tuned in for its opinion hosts.

So, for instance, when Mr. Hannity went to Cincinnati to headline a planned Tea Party event in 2010, the boss forced him to cancel, angry that he had even said yes to such a thing.

.. These days, it seems, Fox News doesn’t have anyone drawing the line. It has been that way since the departure of Mr. Ailes, who was booted from the network in 2016 after multiple women accused him of sexual harassment and who died the next year.

• .. Mr. Hannity has called the investigation by the special counsel, Robert S. Mueller III, part of a “deep state” conspiracy run by a “crime family.”
• Laura Ingraham has likened the federal detention facilities holding migrant children to “summer camps.” And
• Tucker Carlson has described the caravan of asylum seekers as “highly dangerous.”

.. Ainsley Earhardt, a “Fox & Friends” host, did not score one for journalism when she offered an on-air defense of Mr. Trump’s use of the phrase “enemy of the people” to describe the news media. “He’s saying: ‘If you don’t want to be called the enemy, then get the story right. Be accurate and report the story the way I want it reported,’” Ms. Earhardt said.

.. I have yet to see Rachel Maddow showing up at a campaign event for Nancy Pelosi or Chuck Schumer.

.. The morning after the rally in Missouri — after in-house complaints from anchors and reporters and a broader social media backlash — the network issued a statement that mentioned neither Mr. Hannity nor Ms. Pirro by name. “Fox News does not condone talent participating in campaign events,” it said, before referring vaguely to “an unfortunate distraction” that had “been addressed.”

.. Two weeks ago, a guest on Lou Dobbs’s show on the Fox Business Network, the conservative activist Chris Farrell, made the false allegation that the liberal political donor George Soros, who is Jewish, had paid migrants to come to the United States; he also asserted without evidence that Mr. Soros had undue influence in the State Department. Those false charges hark back to common anti-Semitic tropes. After deafening blowback, Fox News said Mr. Farrell would no longer appear on its channels.

.. And earlier this month, Ms. Pirro headlined a fund-raiser for Scott Wagner, the Republican candidate for governor in Pennsylvania. As The Philadelphia Inquirer reported, she earned $24,500 for serving as an “event speaker.” (Fox News had no official statement on that one.)

.. The only guardians of the old rules separating Fox News journalists from the people they are supposed to cover are the working journalists at the network. Apparently fed up with the caravan hysteria promoted by the prime-time pundits, the Fox News anchor Shepard Smith said on-air, “There is no invasion. No one is coming to get you. There is nothing at all to worry about.” Others, like the Fox News anchor Bret Baier and the Sunday host Chris Wallace, have at times made public complaints. As Mr. Wallace once said about the network’s pundits parroting Mr. Trump’s anti-press attacks, “It bothers me.”

..  When companies pulled their commercials from “The Ingraham Angle” after its host poked fun at David Hogg, a student survivor of the mass shooting in Parkland, Fla., the show’s ratings went up.

.. Administration officials with former on-air roles at the network include Ben Carson, the housing secretary; John Bolton, the national security director; Heather Nauert, the State Department spokeswoman; and Mercedes Schlapp, the White House strategic communications director. Oh, and Mr. Trump’s former communications director, Hope Hicks, has been hired as the communications director at Fox News’s corporate parent.