Over the past few years, chief executives — including prominent figures like Lloyd Blankfein of Goldman Sachs and Howard Schultz of Starbucks — have been taking public stances on controversial issues like race relations and gender equality that are unrelated to their core businesses. It’s headline-grabbing stuff. But is it politically effective?

Anecdotal evidence suggests so. On Monday, for example, after public pressure from the chief executives of Intel, Salesforce.com and Unilever, Gov. Nathan Deal of Georgia, a Republican, announced his intention to veto a “religious liberty” bill that would allow faith-based businesses and nonprofit groups to discriminate against same-sex couples. And last year, Apple’s chief executive, Timothy Cook, publicly opposed a similar bill in Indiana. In the end, Gov. Mike Pence, a Republican, signed a revised version of the law that specified it would not allow discrimination based on sexual orientation or gender identity.

There is a long history of corporations’ wielding influence on public policy through lobbying, but C.E.O. activism is newer and less understood. Because there has been little, if any, research on it, we recently conducted an experiment about its impact. Our findings, reported in a working paper released last month, suggest that C.E.O. activism can sway public opinion — and also increase interest in buying the company’s products.

We worked with a market-research company called Civic Science that collects thousands of survey responses every day using hundreds of third-party websites (newspapers, entertainment sites and so on). We asked nearly 3,400 respondents across the country whether they supported Indiana’s “religious liberty” law. For some respondents, the question was prefaced with an unattributed statement that some people worried that the law would allow discrimination against gay men and lesbians. For other respondents, that statement was attributed to Mr. Cook of Apple; or to William Oesterle, the C.E.O. at the time of the Indiana-based company Angie’s List; or to the mayor of Indianapolis.

We found that public support for the law declined sharply, and roughly equally, if respondents were informed that Mr. Cook, Mr. Oesterle or the mayor of Indianapolis was concerned about it. This provides some evidence that prominent chief executives — even when they aren’t major employers in the state — can shape public opinion about controversial social issues. Mr. Oesterle, after all, could credibly commit to moving jobs out of Indiana, and the mayor of Indianapolis can claim to understand the needs and values of people in Indiana. But Mr. Cook apparently also commands a sizable audience that can be swayed by his opinion.

Perhaps more interesting, we asked another 2,176 respondents how likely they were to buy Apple products. We prefaced this question for some respondents with information about Mr. Cook’s discrimination concerns, for others with a description of Mr. Cook’s business philosophy and for the remainder without any preamble. Respondents who were prompted by Mr. Cook’s opposition to the Indiana law — particularly those who supported same-sex marriage — expressed a greater intent to purchase Apple products than did the other two groups. While it might not be the motivation of C.E.O. activists, consumers appear to respond favorably to the companies’ products when they agree with the chief executive’s politics.

These consumer gains outweighed, in our study, the consumer losses incurred by those who opposed same-sex marriage and were put off by Mr. Cook’s advocacy. This finding brings to mind Dan T. Cathy, the chief executive of Chick-fil-A, who in 2012 angered many progressives with public comments opposing same-sex marriage — but who also received plaudits, and perhaps increased business, from those who agreed with him.

Our findings are preliminary. But if they turn out to hold more broadly, they may signal a major shift in corporate public relations. Until recently, most large companies aimed to be neutral on controversial social issues, not wanting to alienate a large segment of potential customers. As the basketball star and Nike pitchman Michael Jordan memorably said when he declined to endorse a Democratic candidate, “Republicans buy sneakers, too.”

But in an era of political polarization, in which we are increasingly cloistered in neighborhoods, social networks and workplaces that serve as echo chambers for our ideological beliefs, corporate neutrality may be outdated. As brands seek to “personalize” their relationships with consumers, is adopting a political orientation part of closing the deal? Perhaps it is better in 2016 to be intensely loved by a few than inoffensive to many.

This op-ed appeared in print as a New York Times op-ed on April 3, 2016 in the Sunday Review’s Grey Matter column on page SR10.

Aaron K. Chatterji is an associate professor at the Fuqua School of Business at Duke University, and serves on the Board of Directors of ARCS.

Michael W. Toffel is a professor at Harvard Business School, and is a co-founder of ARCS and serves on its Board of Directors.