Fox News Welcomes Pete Buttigieg. Trump and ‘Fox & Friends’ Aren’t Pleased.

The night began with a campaign-style biographical video and ended with a standing ovation. The candidate called President Trump’s behavior “grotesque” and lamented the “media noise machine on the right wing.” He attacked Tucker Carlson and Laura Ingraham by name.

Viewers of Mayor Pete Buttigieg’s town hall event on Sunday could be forgiven for thinking they had stumbled onto an hour of prime-time MSNBC.

Nope. This was Fox News.

The network that liberals love to hate wants to be a required pit stop for Democrats running in the 2020 presidential primary. And despite a snub last week from Senator Elizabeth Warren of Massachusetts, who denounced the channel as a “hate-for-profit racket,” Fox News is finding some success.

Mr. Buttigieg’s hourlong appearance spawned headlines, solid ratings, and kudos from liberals pleased to see the South Bend, Ind., mayor calling out Fox News pundits on their own network.

.. The reaction was chillier among some of the network’s core conservative viewers — including one miffed resident of the White House. “Hard to believe that @FoxNews is wasting airtime on Mayor Pete,” President Trump wrote on Twitter before the town hall event began. “Fox is moving more and more to the losing (wrong) side in covering the Dems.”

At a rally in Pennsylvania on Monday night, the president kept up his criticism. “What’s going on with Fox, by the way? What’s going on there?” Mr. Trump asked the crowd, which responded with boos. “They’re putting more Democrats on than Republicans. Something strange is going on at Fox, folks.”

.. “It’s clear their audience is split on whether it was a good idea to offer Buttigieg airtime,” said Eric Bolling, a former Fox News star who now hosts “America This Week” for the Sinclair Broadcast Group.

Fox News has stayed uncharacteristically quiet about the reception to its Democratic town hall events. The network refrained from hitting back at Ms. Warren’s attack last week, and it declined to comment on Monday about Mr. Trump’s taunts.

On Sunday, Mr. Wallace, who was moderating Mr. Buttigieg’s town hall event, was again in the spotlight. Mr. Trump, in his pre-emptive tweet, compared the anchor unfavorably with his father, the former “60 Minutes” host Mike Wallace, and knocked him for praising Mr. Buttigieg’s “substance” and “fascinating biography.”

“Gee,” Mr. Trump wrote, “he never speaks well of me.”

That prompted a rare rebuke from Brit Hume, the Fox News senior political analyst. “Say this for Buttigieg,” Mr. Hume tweeted at the president. “He’s willing to be questioned by Chris Wallace, something you’ve barely done since you’ve been president.”

Mr. Hume added, “Oh, and covering candidates of both parties is part of the job of a news channel.”

“If you want to counterprogram Fox, you have to do it to their face,” said Lis Smith, who runs Mr. Buttigieg’s communications strategy. “We can’t just retreat to our self-reinforcing echo chambers.”

“If you want to talk to every voter, you have to meet them where they are,” Ms. Smith added.