Is Elon Musk misunderstood, or understood all too well?

That was essentially the message he took to Cannes, France, this past week in an effort to repair things with advertisers after telling some of them to “go f— yourself" back in November.

His advocates relayed a similar message of it’s just a misunderstanding to Wall Street after Musk said he didn’t feel comfortable working on AI at Tesla without a bigger ownership stake.

For one of the world’s richest men, with one of the world’s largest social-media networks as a megaphone, Musk seems to miscommunicate a lot.

He is a billionaire who built his reputation partly on having no filter, fueling a perception of authenticity that appeals to supporters who like his contrarian bets and lack of conformity.

“If you’re a normal human being and you speak freely, there are times when you will say things that you subsequently regret or are foolish," Musk said in France. “But if you’re constantly going through a filter, now you’re not being real. So I guess I think it’s better to be real than to go through a filter."

What was once celebrated as authentic, however, is presenting new risks to his businesses today. Advertisers have become wary of X. Some Tesla buyers have been turned off by his contentious stances.

Musk has essentially chalked things up to misunderstandings before—like when he claimed “funding secured" to take Tesla private when, in fact, a buyout wasn’t a done deal. Or the time he called a cave explorer involved in rescuing a Thai youth soccer team a “pedo." Or when Musk surprised many with an announcement in 2019 that Tesla would begin shutting physical retail locations, but then quickly scaled back such plans.

“I didn’t handle messaging of that well," Musk later told analysts. “We make a statement—it’s sort of taken to an extreme [then] there’s a misunderstanding."

Increasingly, his backtracking makes it challenging to know when to take him seriously, effectively watering down some of his authenticity. All of which comes at a bad time for Tesla, where the chief executive officer is trying to plot a bold new future to satisfy investors worried about falling electric-car sales.

Among his newest predictions: telling Tesla investors recently that the automaker’s valuation could soar to more than half of the combined value of the S&P 500 thanks to future humanoid robots like C-3PO in the “Star Wars" movies.

He made the statement to investors, some of whom had worried he would leave Tesla if they rejected a recent proxy proposal to reapprove his 2018 pay package. Their concerns were rooted in earlier tweets in which he suggested a willingness to take his best ideas elsewhere without an increase in ownership in Tesla.

“I am uncomfortable growing Tesla to be a leader in AI & robotics without having ~25% voting control. Enough to be influential, but not so much that I can’t be overturned," Musk tweeted in January. “Unless that is the case, I would prefer to build products outside of Tesla."

Ahead of the annual meeting on June 13, when the vote in favor of the pay plan was announced, some Musk supporters, including Travis Axelrod of Tesla’s investor-relations department, quietly worked to seed the idea that Musk’s comments were being misunderstood.

“Mr. Axelrod regretted there had been some misunderstanding regarding Mr. Musk’s desire for control of 25% of Tesla’s voting shares…suggesting this desire is motivated primarily by the wish to protect humanity from the potentially negative implications of imprudent or improper use of AI technology," Ryan Brinkman, an analyst for JPMorgan, told clients in a note following a meeting with Tesla.

Critics of Tesla have suggested that Musk’s comments about building outside the company could come back to bite him in court. The shareholder whose lawsuit resulted in the move by a Delaware court earlier this year to rescind the original 2018 pay package might argue that the CEO was effectively threatening investors.

The “plaintiff may argue that the entire shareholder vote is ineffective because it was orchestrated entirely by Musk, using a coercive process in which he, in effect, extorted the favorable votes under threat of further stripping Tesla of its artificial intelligence and robotics capabilities," Lawrence Fossi, a longtime critic of Tesla and retired commercial lawyer, wrote in an analysis of the pay-vote results.

On stage this past week at the important ad industry gathering in France, Musk appeared intent on softening things there as well.

After saying that his attacks weren’t leveled against “advertisers as a whole," Musk aimed to make the case for why advertising on X was worth it and detailed what he, himself, thinks is a valuable kind of advertising. Uncharacteristically, he even briefly waxed almost admiringly about how Vogue magazine is filled with “beautiful ads."

It would be easy to see why advertisers might have been surprised, especially if they had read his past tweets, such as in 2019, before owning X, when he posted: “I hate advertising."

On stage, Musk said, “I’m actually a fan of advertising that is artistically interesting, that is entertaining. Really, the acid test being when after you see the ad, do you regret seeing the ad?"

Of course, Musk now owns X and is an interested party in trying to revive ad spending on the platform. Brands pulled back after Musk in November amplified a tweet supporting antisemitic vitriol, and Media Matters for America, the left-leaning media watchdog group, claimed big-brand ads were running near hate speech (which X has disputed as a misleading portrayal). In the midst of that pullback, he publicly lashed out with the “go f— yourself" remarks.

In the past, Musk has suggested that sometimes people read too much into what he says.

“People shouldn’t hold me to these things," Musk said in 2022 during a TED Talk interview. “What tends to happen is I’ll make some like, you know, best guess, and then people in five years, there’ll be some jerk that writes an article: ‘Elon said this would happen, and it didn’t happen. He’s a liar and a fool.’"

“It’s very annoying when that happens," Musk continued. “These are just guesses, this is a conversation."

Still, he is the CEO of a public company, and his best guesses move markets. His mere tone of voice on investor calls has been known to send Tesla stock up or down depending on his perceived mood about the future.

If Musk severely loses credibility—his comments become merely met with eye rolls and, “Oh, that Elon"—the risk is that his power to inspire fades, too.

Write to Tim Higgins at tim.higgins@wsj.com