You seem to be bundling freedom of speech with freedom from the consequences of that speech.
Actually, no. The latter contradicts the former. One cannot truly speak freely if one has to be mindful of the consequences. This is fine in principle but the manner in which the consequences are decided is often dubious at best, whether the person speaking is in the "right" or "wrong".
Nobody is forcing them to keep quiet, just now some people may begin to accept that others may not want to do business with organisations headed by people they consider bigoted.
Making an example of someone for speaking is likely to make others think twice before speaking, no? Once again, the person speaking could be in the right or wrong, the principle is the same.
I don't purchase goods or services from known tax avoiders or organisations which score poorly based on local & environmental impact (ethical business index), this is no different really.
Well it is a little because the examples you give imply an ongoing, negative impact, which is lacking from the story in the OP. At best he continued to actively support anti-gay legislation but we are unaware of it. At worst, he no longer believes that way but does not feel the need to justify himself to the baying mob. Although I imagine the truth is somewhere in between.
There is also the matter of the extra step of singling him out and demanding he step down, whilst doing so publicly. Seeking to force a person to step down for past "misdeads", if applied to those of more limited means, has the potential to destroy livelihoods.
Nobody is saying you can't believe that, just that others may challenge that belief if & if you pushed them while being the head of a large organisation you should expect some media fallout (which may result in you getting pushed out the door).
And yet if he had used more discreet methods to drum up support (which he may well have done as well), then voted without declaring it publicly, he would have gotten away with it. He is not so much being punished for his views as his indiscretion.
You are free to believe that marriage should be between just a man & a women - but you are not free to project that view onto the lives of others & expect them to conform to it.
Personally, I don't care what people think - I care what they do.
You are indeed free to think what you like, but you are not free to do what you like (deny equal rights to others in this case).
Actually, as long as you do it within the established and legal system for creating, changing and abolishing legislation, you are most definitely free to do just that. Indeed, judging by the narrow margin that Prop8 passed by, a little over 50% of people voting did just that. The fact that another part of that system later struck it down is beside the point.
But it is worth bearing in mind what actually happened here. A person is not being accused of sending the boyz round to gay weddings, in order to lynch the attendees. He is not even accused of making homophobic comments in public. He simply exercised his legal right to participate in the debate between two sides on contentious issue, but happened to choose what a sufficiently vocal minority (and many other who do not care enough to act against him) hold to be the wrong side. Edit: Not to suggest that only a minority would disagree with him but it is the vocal minority who acted, therefore the rest are not so relevant here.