That is incorrect. Any company must act in the best interest of its shareholders. A publicly-traded company must maximize profit because that's the implicit nature of it: I buy stock in the market because I want a return on my investment. But if all shareholders of a given company (say, Mozilla) want to produce something for the good of the Internet and not make a profit, that's up to the shareholders.

A "non-profit" status simply gives the organization certain tax advantages because the state understands that the organization is acting on the best interest of the community, rather than its shareholders. But if a for-profit wants to do the same and not take advantage of said tax benefits, that's up to the shareholders to decide.

http://biztaxlaw.about.com/od/glossaryf/g/fiduciary.htm

You're confusing "for-profit" and "publicly traded". It's commonly held that publicly traded companies should be maximizing shareholder value (which is not necessarily the same as profit), because that's the purpose of publicly traded corporations.

There are also various protections for minority shareholders in privately held companies to prevent majority shareholders from screwing them over.

And there are various rules about how the company's officers need to pay attention to the shareholders.

In this case, there is precisely one shareholder: the Mozilla Foundation. So the various minority-shareholder protection stuff does not apply, but the officers of the Mozilla Corporation do need to pay attention to what the Foundation wants the Corporation to do. And what the sole shareholder wants the Corporation to do in this case is decidedly not to maximize profit.

Except the minor detail that being for-profit does not, itself, imply that the company has shareholders.