Is he a bigot? "A bigot is someone who, as a result of their prejudices, treats or views other people with fear, distrust or hatred." I don't think he does that. He just wrongly thinks the state shouldnt recognize same sex marriage.
It was a ballot initiative in 2008. We have a constitution to prevent the will of the majority violating the rights of a minority. Its too bad it was up to voters. But he still has a right to take a side without fear of economic retribution.
Economic retribution from the government the first amendment does not protect your rights with respect to things like keeping a job. If you call your boss an asshole to his face on a regular basis, you are going to be fired.
Which is why we have laws (separate from the amendments) which ensure people can't be fired for their race/gender/etc. These laws have nothing to do with the first amendment because they don't involve the government.
Liberals would not like it if the Catholic Church used its members to lobby for a person to be fired for their stance on abortion. Don't use Firefox, fine. But actively lobbying to take away someone's livelihood is not a proportional response in this case.
I'm ignoring your partisan labelling/strawman/etc.
On the second point, that's why employers aren’t allowed to ask those questions (nor use them in their evaluation of employees). Those are the protection laws I mentioned above. Which don't protect executive members, as they run the company. Hence employees shouldn't, and can't, be fired for their political opinions (unless that's somehow part of their job).
Proportional response? Sure. Here is a guy who paid money to make it so people can't see their significant others when they are dying, so that they don't have the recognition of the government as being married, to institutionalize oppression, and the untold misery which comes with it. He didn't apologize, he still holds the same views now. Yes, people should lobby a company, any company, to remove someone who would inflict such misery on his fellows. Yes, people should lobby a company like mozilla which says its an avid supporter of freedom to remove someone who would not support equal freedoms for every single person. These companies are corporate citizens, and their opinions are shaped by their executive board, and we can tell them we won't do business with them because of their opinions.
Edit: If you read the above, the response to the question should be obvious. Is it a board member? Then sure, good luck with that though, considering they would loose business if they followed the complaints, but not loose any if they ignored them (yea hospitals don't really care about customer retention). If it's an employee, and that employee didn't do anything wrong (like say, perform an abortion when not asked to; or badger someone with their political view) then no.
It was trivial amount of money for an $83MM campaign. It may signal which side of the issue he was on. It does not inform us of what he is thinking or his motivations.