I disagree sempai. Holding a CEO to a different standard than a common employee is a recipe for elitism.

I will reiterate that a person's beliefs have no bearing on their ability.

You hold CEOs to a different standard because they are the public face of an organization; their personal brand impacts the brand of the company. That's not elitism, that's common sense. If a common employee holds some unpopular opinion, why should anyone care? But if the CEO does, it damages the company, and the company should care about that.

Well, and go one further: if a common employee does hold an unpopular opinion and they publicize it widely, think how long they'll last at the company anyway.

Take a totally fictional example, a product manager at Intel who, on the weekends, has been leading neo-nazi marches and getting on the news. The reporters ask him, "what do you do to pay for all these flags and banners and tattoos?" "Oh, I work at Intel during the week. I'm a product manager in the networking hardware division."

Think how many weekends they'd give out that interview answer before Intel let them go for whatever reason.