There's some productive digging to be done there, but I've got work to get back to! Maybe another time.
I agree with that, but I also think a public comment about a personal belief can interfere with a job that involves speaking on behalf of others. When ones publicly known personal beliefs conflict with the beliefs one expresses while doing ones job, it causes a severe credibility problem, at least.
I'd say the other factor you mentioned is the conflict between "personal" statements and "official" statements. Some people do seem to be able to manage that, in part by avoiding uncompromising statements like "bread is terrible, no one should buy it". In your example, the conflict was so obvious and so provocative that it would be untenable and render the job of CEO impossible.
What does it mean, then, to say we shouldn't police beliefs? I'd say it means we shouldn't police actions that are only expressions of personal belief.
"Personal" is important when we consider people, like CEOs, who speak for the company. The board has a right to expect the CEO to speak for them, and the shareholders, in turn, to elect a board that speaks for them. A CEO who officially says "bread is terrible, no one should buy it" has failed to perform that job. A CEO who says the same thing unofficially, or before being hired, won't be able to credibly perform the job.
A salesperson would have the same problem. The job demands saying "you should buy bread". Saying the opposite makes it impossible to perform the job, if the people you're dealing with learn about it.
OTOH, if a bakery worker or secretary, for example, says "bread is terrible, no one should buy it, I only work here because I need the money", I would defend their right to express their beliefs. If they were fired I'd consider that unjust.