No, he must act in good faith when acting in his capacity as a board member and corporate officer. When acting in his capacity as a shareholder, he has no such obligation. The line between the two roles is usually pretty clear.

Think of a member of a military. They have a clear duty to act according to the policy and orders of their superiors. But in most nations, they can also vote, in their personal capacity as citizens, to change the top level of leadership, and they have no obligation to exercise their vote in furtherance of anyone's agenda but their own.

Zuckerberg's position is similar. What's out of whack is that he controls a majority vote of the "citizenry" (shareholders) himself.