Times have changed. With Megyn Kelly and Bill O’Reilly gone from Fox News, Mr. Hannity is its undisputed prime-time star, and his “Trump at all costs” brio is the template for a network that has tacked rightward since Election Day.
That Mr. Hannity failed to disclose an entanglement with a prominent Trump consigliere — particularly one at the center of a federal criminal investigation — did not sit well in some corners of the Fox newsroom, especially among reporters who have expressed displeasure with the White House access enjoyed by the channel’s Trump-boosting commentators.
In an official statement, however, the network stood up for its star, saying: “We have reviewed the matter and spoken to Sean and he continues to have our full support.”
Not every Fox News host is so immune.
Bret Baier, the network’s 6 p.m. news anchor, presents himself as a staid newsman compared with the channel’s boisterous crew of partisan pundits.
But after Politico reported on Monday that Mr. Baier played nine holes of golf with Mr. Trump this past weekend at the president’s Virginia club — the kind of chummy socializing that is considered poor form for journalists — the anchor found himself in hot water.
Asked on Tuesday about the golf game, Fox News said that the network’s president of news, Jay Wallace, “addressed the matter” with Mr. Baier.
It is not unusual for anchors to schmooze politicians for access, and Mr. Baier has been jockeying for an interview with Mr. Trump, who has not appeared on his show since October 2016. But several TV journalists and former White House officials said they could not recall another instance of an anchor golfing with a president.
Adding to the unease: the White House often refuses to disclose Mr. Trump’s golf partners, or that he is hitting the links at all, drawing concerns about a lack of transparency.
Fox News has different ethical standards for its news and opinion anchors, and Mr. Hannity, firmly on the opinion side, has a longer leash.
He has offered Mr. Trump advice, parroted his sulfurous attacks on the media, and dined with him at Mar-a-Lago and the White House. Like other cheerleading Fox pundits, including Jesse Watters and Jeanine Pirro, Mr. Hannity has been granted a presidential interview multiple times.
It has been good for business. In early 2016, “Hannity” averaged 1.8 million viewers and was the sixth-most watched show on cable news. This year, he is averaging 3.2 million viewers — and is ranked No. 1. On Monday, his first show since the revelations about Mr. Cohen, Mr. Hannity pulled in 3.7 million viewers, topping his MSNBC rival, Rachel Maddow, and two N.B.A. playoff games.
Those numbers are the envy of the industry, even as rival hosts have increasingly lamented Fox News’s hard-line turn.
In February, the NBC News anchor Chuck Todd wondered aloud if the network’s ethics standards had deteriorated since the 2016 exit of Roger E. Ailes, the network’s late mastermind. “I can’t believe that I’m about to say what I’m about to say,” Mr. Todd said on a Recode podcast. “But Roger Ailes ran a more journalistically honest organization.”
News organizations have dealt with anchors’ ethical lapses in varying ways.
MSNBC suspended the liberal commentator Keith Olbermann in 2010 after it learned that he made campaign donations to Democratic congressional candidates. ABC News backed George Stephanopoulos, its chief news anchor, after he apologized for not having disclosed $75,000 in donations to the Clinton Foundation, saying, “We stand behind him.”
As for Mr. Hannity, an unlikely ombudsman popped up on his show this week. The lawyer Alan Dershowitz, a regular guest, confronted him on the Monday edition of “Hannity,” telling the host that “it would have been much, much better had you disclosed that relationship.”
In an interview on Tuesday, Mr. Dershowitz said he had felt compelled to say something because Mr. Hannity had included him in a live discussion of Mr. Cohen’s legal troubles last week. “When you are talking to millions of people every night, you should make a full disclosure,” he said.
But Mr. Dershowitz added that Mr. Hannity did not necessarily deserve to be disciplined.
“The Fox viewers didn’t suffer from his failure to disclose,” he said. “Why? Everybody who watches Hannity knows who he is, and knows what his views are. He wouldn’t have said anything different.”
“Whether I’ll ever be invited back to Hannity’s show, I don’t know,” Mr. Dershowitz added. “But I had to make my point.”