Mr. Hume added, “Oh, and covering candidates of both parties is part of the job of a news channel.”
Viewers have tuned in, too. About 1.1 million people watched Mr. Buttigieg on Sunday. Senator Amy Klobuchar of Minnesota drew 1.6 million viewers earlier this month. Senator Bernie Sanders’s Fox News town hall event was seen by 2.5 million people, the biggest TV audience yet for a candidate for the Democratic nomination. A Fox News town hall with Senator Kirsten Gillibrand of New York is scheduled for next month.
On Sunday night, Mr. Wallace did not contradict Mr. Buttigieg’s criticisms of Mr. Carlson and Ms. Ingraham. But even he seemed surprised at the warm reception for the mayor, exclaiming “Wow!” when the audience stood up to applaud at the end.
Mark McKinnon, a veteran political strategist, said he could understand why Mr. Trump might be alarmed at seeing potential rivals show up on his favorite network.
“Anyone who goes to a Fox town hall is going to come off better, more reasonable, more human, and not nearly as evil, ideological or stupid as they are currently being painted by the network,” Mr. McKinnon said. “The bar is low. Viewers will be pleasantly surprised when Democrats show up to town halls and they’re not wearing Mao caps.”
For Ms. Warren, such distinctions are moot. In opting out of a town hall event, she declared Fox News a propaganda outlet for the president and said that Democrats who go on the network only help its reputation and bottom line. Senator Kamala Harris of California has also announced a boycott.
Ms. Warren and Ms. Harris won plaudits for their stance from some liberals. But other Democratic campaigns say the channel remains a key venue to reach voters outside the party’s base.
“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.