By Matt Egan, CNN

(CNN) — Brands are being “irresponsible” by continuing to advertise on Elon Musk’s X after the billionaire endorsed antisemitic views, according to Yale professor Jeffrey Sonnenfeld.

“It’s self-destructive for any advertiser to be associated with him. It’s pathological,” Sonnenfeld, dean for leadership studies at the Yale School of Management, told CNN in a phone interview.

Musk set off another round of controversy last week by agreeing with an antisemitic post on X that claimed Jewish communities push “hatred against Whites.” Musk responded by saying: “You have said the actual truth.”

Some major brands have halted advertising on X (formerly known as Twitter), including Disney, NBCUniversal and CNN owner Warner Bros. Discovery. Those advertisers did not specifically say the decision was linked to Musk’s post, though some of their ads were found to be placed near antisemitic posts on X, according to a report by progressive watchdog group Media Matters.

“There should be no public company advertising on Twitter. You can’t have someone endorsing replacement theory and be associated with that,” said Sonnenfeld. (Replacement theory, popularized in far-right White nationalist circles, argues Democrats and liberals are plotting to import undocumented immigrants to reduce the political power of White people.)

Joe Benarroch, head of business operations at X, responded by telling CNN in an email: “Jeffrey Sonnenfeld must not believe in free speech.”

In a blog post on Friday, X accused Media Matters of aggressively searching for pro-Nazi content in a way that “misrepresented the real user experience” and could “mislead advertisers.” Musk has also filed a lawsuit against Media Matters, a legal battle that the group says it can win.

Yaccarino under pressure

The advertiser backlash is piling even more financial pressure on X at a time when the social media platform has been struggling. And it’s causing another massive headache for X CEO Linda Yaccarino, the former NBCUniversal executive who joined the company earlier this year to help boost its ad business.

“Linda Yaccarino should resign,” Sonnenfeld said in the interview. “As talented as she is, unless she can force (Musk) to recant his words, which he’s not going to do, she should give up.”

Some advertisers are trying to persuade Yaccarino to do just that.

Marketing industry veteran Lou Paskalis previously told CNN there has been a “groundswell” of ad execs urging Yaccarino to step down.

However, Yaccarino has signaled she doesn’t plan to quit, posting on Monday morning: “I believe deeply in our vision, our team and our community.”

A marketing dilemma

Nell Minow, vice chair of ValueEdge Advisors, which advises institutional investors on corporate governance, argues the free market will sort out the mess at X.

“This is a perfect opportunity for the market to do what the market does best,” Minow said. “If advertisers don’t want to put an ad in an environment that won’t enhance their product, they will withdraw. It’s like: Do you want to have your ads run in Time Magazine or Hustler?”

Even though X is no longer a public company, Minow said there could still be consequences for Musk.

“If other investors and those who hold the debt start to feel iffy about the financial prospects, they will hold him accountable,” Minow said.

Tim Calkins, a marketing professor at Northwestern University’s Kellogg School of Management, said brands don’t need to “completely agree” with a media property and its policies to advertise there.

Still, Calkins said it’s becoming increasingly hard to separate Musk from X’s controversial comments and noted concerns about how the social media platform polices content.

“The last thing a brand wants is to spend money to unintentionally get pulled into a polarizing topic,” Calkins said.

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