CEOs of major U.S. companies have reason to be worried about growing shareholder unrest on a range of social issues.

Although shareholder complaints can come in a variety of forms, such as boycotts and pressure through social media, shareholder resolutions have been the primary means for shareholders to voice their concerns and demands. Among other things, they demand that corporate leaders improve diversity efforts, change product portfolio, reduce their environmental footprint and speak out about politics.

CEOs ignore these shareholders at their own personal peril. According to new research I have conducted with colleagues Michelle Lee of Queen’s University (Canada) and Don Hambrick of Pennsylvania State University, disappointing shareholders on these social issues can be highly—and sometimes fatally—damaging for the career of the CEO.

In fact, our study found that CEOs who riled shareholders on social issues were more likely to receive compensation penalties and be fired than when shareholders were unhappy about the CEOs’ wealth-oriented actions, such as those focused on strategy and governance. Surprisingly, shareholders’ wealth-oriented concerns had a negligible effect on CEOs’ compensation and dismissal prospects.

Why would this be so? Why would shareholders’ complaints about social issues be more damaging to CEOs’ careers than those about wealth-maximizing concerns? After all, most shareholders typically buy the stock of a company to make money—not to change the world.

The explanation, we believe, comes from the study of “information economics.” It suggests that if you give people information that simply corroborates what was previously known, those people would think of the information as redundant, and wouldn’t change their opinions.

That’s why shareholder unrest focused on corporate social responsibility is much more potent than unrest focused on wealth maximization. There are many well-established financial metrics—such as stock returns, net income and sales growth—that speak to how well CEOs are fulfilling their wealth-maximization duties. Thus, shareholders’ wealth-oriented unrest may be less consequential in the eyes of a company’s directors, who already have incorporated those metrics in their thinking about the CEO’s pay and future.

In contrast, measuring the degree to which a company is fulfilling its corporate-social-responsibility obligations is notoriously tricky. There are no universally agreed-upon metrics of a company’s social performance. Whether a company is sufficiently reducing carbon emissions and whether it adequately promotes diversity and inclusion are widely debated in both academic and business circles. Shareholder unrest focused on social issues, therefore, is new information for the board, which may fear that the company is at risk of suffering negative press and reputational damage.

Share Your Thoughts

How should CEOs balance social and financial concerns? Join the conversation below.

The impact, though, goes even beyond the individual CEO. Shareholder unrest not only may result in the targeted CEO leaving the firm but also affects the firm’s ability to hire a suitable replacement. When a CEO leaves in the aftermath of shareholder unrest, it conveys to all the potential CEO candidates that they should expect to inherit some of the predecessor’s challenges. Those candidates will likely worry about being set up for failure.

As a result, we find, the company has to offer a heftier pay package to the new CEO, relative to both the predecessor’s and those of other CEOs joining comparable firms.

Findings from our study offer lessons for both CEOs and shareholders. CEOs need to pay greater attention to shareholders’ concerns and try to prevent shareholder unrest from arising. If shareholder unrest does occur, CEOs should particularly take heed of corporate-social-responsibility concerns, as they are likely to have a more significant impact on their career than concerns related to wealth maximization.

For shareholders, it is worth keeping in mind that while shareholder resolutions allow them to exercise power, they may also create costs that they will ultimately bear. If the shareholder unrest escalates substantially, it will raise the cost of executive talent for the firm and add to what is already a pretty steep burden of hiring qualified CEOs.

Dr. Gupta is an associate professor of management at the Michael G. Foster School of Business at the University of Washington. He can be reached at reports@wsj.com.