I did not approve of the pressure against Brendon Eich, CEO of Mozilla, even though I thought he supported a hateful and divisive cause. He was one of the founders of the company and what he did was personal, not while wearing his Mozilla hat. I will grant that a CEO is not like an hourly employee, however, he or she is the public face of the company. When the public face of the company becomes associated with bigotry and discrimination, that becomes a problem for that company’s image, so there is at least a somewhat valid reason for his departure.
However, when you are Dropbox, a company that stores the data for millions of individuals and companies and the new member of your board of directors is a torture apologist who is on record supporting warrantless wiretaps, that is a direct threat to me and my expectations of privacy. Board members don’t manage the day to day operation of a company, but they certainly help determine the direction the company is heading and have significant influence on company policies, including whether they just hand over customer data to any government official who wants it or if they fight it tooth and nail. I won’t do business with Dropbox as long as Condi Rice is on their board of Directors. So I guess the answer to your question, at least for me, is that it depends on the individual circumstances.