Look at it this way. If at the time of the invasion of Iraq, people suddenly noticed Eich had donated to an anti-war cause, or maybe mentioned in private that he thought 9/11 was a consequence of US foreign policy, how many red-blooded, freedom-fries eating Americans would have asked for his head because he held an unpopular opinion?
I'm not aware of any case, but it's possible. You may have examples during the Vietnam war or the Red Scare. The basic issue is the same, though: is it OK to let the Vox Populi evict a CEO for holding currently unpopular views?