Democratic presidential candidate Sen. Elizabeth Warren (Mass.) last month declined an invitation from Fox News to appear at a town-hall event. “Hate-for-profit works only if there’s profit, so Fox News balances a mix of bigotry, racism, and outright lies with enough legit journalism to make the claim to advertisers that it’s a reputable news outlet. It’s all about dragging in ad money — big ad money,” said Warren in turning down the invitation.

On his Friday night program, Tucker Carlson proved her right. The Fox News host conducted a discussion with radio host Larry Elder pegged to Warren’s recent appearance with radio host Charlamagne Tha God, in which she was asked about the controversy over her having claimed American Indian heritage. At the end of the discussion, almost as a throwaway comment, Carlson riffed, “She’s nasty, too, unfortunately. She shouldn’t be. She is, though. She is nasty.”

Sexist remarks sting most when they’re delivered as an afterthought.

In sliming Warren, Carlson established some affinity with Donald Trump, who used the descriptor in an October 2016 presidential debate. Asked about her economic policies, Hillary Clinton said she’d raise taxes on the rich: “My Social Security payroll contribution will go up, as will Donald’s, assuming he can’t figure out how to get out of it,” Clinton said. Trump talked right over Clinton, commenting, “Such a nasty woman.”

“Nasty woman” thus took its spot on “resistance” T-shirts and paraphernalia. At a campaign stop for Clinton, Warren said, “Nasty women are tough. Nasty women are smart, and nasty women vote.”

The general topic of women, Fox News and decorum emerged again on Sunday night, as Democratic presidential candidate Sen. Kirsten Gillibrand (N.Y.) participated in a town-hall event moderated by Fox News host Chris Wallace. Asked about her stand on late-term abortions, Gillibrand decided that a comprehensive response required hauling in the host network. She voiced her view that intimate “life and death” decisions belong to women. “What we have created, unfortunately, is a false choice and a false narrative. And Chris, I want to talk about the role that Fox News plays in this because it’s a problem. I can tell you before President Trump gave his State of the Union, Fox News talked about infanticide. Infanticide, it doesn’t exist,” said Gillibrand.

The critique prompted what will doubtless prevail as one of the low points in Wallace’s career. “Senator, I just want to say, we’ve brought you here for an hour,” said the host. “We’ve treated you very fairly. I understand that maybe to make your credentials with the Democrats who are not appearing on Fox News you want to attack us. I’m not sure it’s frankly very polite when we’ve invited you to be here.”

Bolding added to highlight the fact that a televised town hall is not Thanksgiving dinner. Nor is it the role of Gillibrand to be “polite” when discussing life-or-death issues. “Instead of talking about Fox News, why don’t you answer [the] question?” implored Wallace.

Instead, Gillibrand doubled down. “The debate about whether or not women should have reproductive freedom has turned into a red-herring debate. And what happens on Fox News is relevant because they talked about infanticide for 6.5 hours, 6.5 hours right before President Trump’s State of the Union [address]. Mentioned it 35 times. That is not the debate of what access to reproductive care is in this country. It doesn’t happen. It’s illegal. It’s not a fact.”

With his appeal to lighten up on Fox News, Wallace looked petty, out of sorts and off base — a strange bit of turf for a guy who’s known for bringing righteous heat upon his interviewees. Gillibrand was right to invoke the role of Fox News in the debate over abortion; the network did, in fact, promote the myth of infanticide in the lead-up to Trump’s State of the Union address. And what Fox News promotes, Trump consumes. In that very real sense, a plea to discuss almost any issue in 2019 without addressing the contributions of Fox News is a pointless one.

In a previous town hall with Wallace, South Bend, Ind., Mayor Pete Buttigieg criticized the commentary of Carlson and fellow prime-time host Laura Ingraham. “I mean, when you’ve got Tucker Carlson saying that immigrants make America dirty. When you’ve got Laura Ingraham comparing detention centers with children in cages to summer camps. Summer camps. Then there is a reason why anybody has to swallow hard and think twice before participating in this media ecosystem,” said the candidate.

It worked out well for Buttigieg, who received good publicity for taking on Fox News while on Fox News. Not even Wallace dared defend the remarks of his opinion-side colleagues.

Next up on the Fox News town-hall circuit is Democratic presidential hopeful Julián Castro, on June 13. Hosts Bret Baier and Martha MacCallum will host the event. We’ll just have to wait and see whether Castro keeps the streak of un-“polite” conduct alive.

Whatever the case, the Democratic candidates are exposing the incompatibility of what Wallace does with what Carlson, Hannity and others do. This blog will never predict dire consequences for Fox News — it’s too profitable to collapse; its viewers are too loyal — but the network’s commitment to playing a central role in the Democratic presidential primary is shedding new light on the fissures of a corrupt news organization.