Short answer: No.
Longer answer: Think Progress reports that:
Starbucks CEO Howard Schultz continued to defend his company’s support for marriage equality at a shareholders meeting Wednesday, pointing out that “not every decision is an economic decision.” Shareholder Tom Strobhar suggested that the company’s stock dipped a bit when the National Organization for Marriage launched a “Dump Starbucks” boycott last year, but Schultz expressed no concern about the company’s viability moving forward:
STROBHAR: In the first full quarter after this boycott was announced, our sales and our earnings — shall we say politely — were a bit disappointing.
SCHULTZ:If you feel, respectfully, that you can get a higher return than the 38 percent you got last year, it’s a free country. You can sell your shares of Starbucks and buy shares in another company. Thank you very much.
Let's say Strobhar sued, claiming that Starbucks' management and board was breaching their fiduciary duties to the shareholders by alienating some customers. Would Schultz et al. have to prove that there were corresponding benefits that outweighed any such losses, such that Starbucks was a net gainer? (After all, a high return is no defense if you could have gotten an even higher one.)
No, of course not. The business judgment rule would stop the suit dead. I am reminded here of Shlensky v. Wrigley, 237 N.E.2d 776 (Ill. App. 1968).
Shlensky challenged Philip Wrigley’s famous refusal to install lights in Wrigley Field. Shlensky was a minority shareholder in the corporation that owned the Chicago Cubs and operated Wrigley Field. Wrigley was the majority stockholder (owning 80% of the stock) and president of the company. In the relevant period, 1961-1965, the Cubs consistently lost money. Shlensky alleged that the losses were attributable to their poor home attendance. In turn, Shlensky alleged that the low attendance was attributable to Wrigley’s refusal to permit installation of lights and night baseball.
In the course of rejecting Shlensky's claim, the court noted that “the effect [of night baseball] on the surrounding neighborhood might well be considered by a director.” Likewise, the court asserted that “the long run interest” of the firm “might demand” consideration of the effect night baseball would have on the neighborhood. (At that time, the corporation owned not just the Cubs but also Wrigley Field and the land on which it stands.) But the court went on to explain that:
By these thoughts we do not mean to say that we have decided that the decision of the directors was a correct one. That is beyond our jurisdiction and ability. We are merely saying that the decision is one properly before directors and the motives alleged in the amended complaint showed no fraud, illegality or conflict of interest in their making of that decision.
Thus, Wrigley did not have to show that his decision was supported by some sort of cost-benefit analysis.
Also on point is the case of Bayer v. Beran, 49 N.Y.S.2d 2, 6 (Sup. Ct. 1944), in which the corporation began sponsoring a opera radio program and hired the CEO's wife to sing on it (along with many others). The court explained that:
To encourage freedom of action on the part of directors, or to put it another way, to discourage interference with the exercise of their free and independent judgment, there has grown up what is known as the “business judgment rule.” ... “Questions of policy of management, expediency of contracts or action, adequacy of consideration, lawful appropriation of corporate funds to advance corporate interests, are left solely to their honest and unselfish decision, for their powers therein are without limitation and free from restraint, and the exercise of them for the common and general interests of the corporation may not be questioned, although the results show that what they did was unwise or inexpedient.” Pollitz v. Wabash R. Co., 207 N.Y. 113, 124, 100 N.E. 721, 724. Indeed, although the concept of “responsibility” is firmly fixed in the law, it is only in a most unusual and extraordinary case that directors are held liable for negligence in the absence of fraud, or improper motive, or personal interest.
The court further explained that "It was for the directors to determine whether they would resort to radio advertising; it was for them to conclude how much to spend; it was for them to decide the kind of program they would use. It would be an unwarranted act of interference for any court to attempt to substitute its judgment on these points for that of the directors, honestly arrived at."
In sum, the fact that shareholders don't like the positions on an issue of public import taken by a corporation states no grounds for legal intervention. Their choices are simple: (1) Try to persuade like-minded shareholders to elect new directors who will take a different position or (2) follow the Wall Street Rule (it is easier to switch than fight).