Here’s a recap: Shortly after taking over as CEO of Mozilla, the open-source computing company known for its Firefox web browser, Brendan Eich found himself on the receiving end of public outrage over revelations that he’d donated $1,000 to anti-gay marriage legislation in California in 2008. Mozilla employees called for his departure and OKCupid notified Firefox users that visited its dating site about Eich’s stance on gay marriage and recommended that they use a different browser.

(As irony would have it, OkCupid co-founder and CEO Sam Yagan once donated to an anti-gay rights congressional candidate.)

Eich resigned on April 3. Upon his leaving the company, Mozilla wrote on its blog that the company “didn’t move fast enough to engage with people once the controversy started. Mozilla believes both in equality and freedom of speech… Figuring out how to stand for both at the same time can be hard.” In essence, Eich’s personal beliefs clashed with Mozilla’s reputation as an open, inclusive community.

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The takeaway: a CEO is a brand unto him or herself; a brand that undoubtedly melds with the company’s own image. If the two don’t mesh, it can spell disaster.

“Whether or not it’s right, it’s not just the [CEO] who holds a certain view. They are blurred with the company, so people assume that the company must also hold that view,” says Ravi Dhar, a marking professor at Yale and director of its Center for Customer Insight. “It’s not unlike what happens in politics. If Obama or Bush holds a certain view, suddenly the rest of the world thinks all Americans believe the same thing.”

The CEO has evolved into a mascot — the human face of a behemoth company. At the same time, business leaders are constantly under scrutiny and any gaffe or controversial statement can spread across the web in the time it takes to type 140 characters.

The confluence of these factors resulted in ruin for Eich, and the precedent set by his experience doesn’t bode well for others, or for the business community overall.

“Unfortunately, it means that CEOs won’t talk as much,” says Dhar. “They’ll become boring since they’ll worry that something they say may inadvertently be linked to the brand.”

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That doesn’t sound like such a bad thing, but it could be bad news for the companies these CEOs lead. A study of CEOs co-authored by Jeffrey Sonnenfeld at the Yale School of Management found that the more charismatic a CEO, the better his or her firm performed financially. Depending on the measure, roughly 10% to 15% of a company’s performance can be attributed to CEO charisma. A 2006 update to the study found that the impact of CEO charisma was greatest in the early years of a chief exec’s tenure — and then the effect tapers off over time. “But it surely did matter,” Sonnenfeld says.

Perhaps these execs can still be extra charismatic, but only on the inside?