You're consistently making a mistake which has its roots in your understanding of "free speech".
I'm afraid you are absolutely wrong about that. I understand the concept of free speech very well and how it is enshrined in the United States Constitution also, Freedom of Speech in the United States is not absolute, and Eich did not infringe on any of those exceptions with his donation to Prop 8, so he rightly retains the right to express himself, and here is the important part you keep ignoring..without fear of persecution or punishment for exercising those rights. By his being subject to a campaign of harassment by a third party (lets jsut call the The Gay Activists for now) he has had his freedoms restricted as he has been effectively punished for expressing his legal constitutional rights, a legal right that is also protected by law under the same constitutional amendment as freedom of speech, that he is free to petition the Government for redress of grievances..which is exactly what Proposition 8 was.
Other citizens' reaction to your free speech does not infringe on your right to free speech. In fact, their reaction is in itself an important facet of free speech.
What they do not have the right to do is to persecute and demand or force punishment for someone expressing their legally protected views. Which is precisely what happened here...it restricts the individual from freely (and that is important) expressing themselves..they are free to criticise or to petition Government to oppose the petition of the individual or group (which is what like-minded people did), but what is wrong is the harassment of Eich after the fact simply because he has an unpopular view.
That Mozilla did not feel that Eich's donation was a matter for them to deal with outside of allowing their staff to criticise or support it as they saw fit until the The Gay Activists (here abetted by OKCupid) publicity stunt and subsequent media attention tells us that initially they saw nothing innately wrong with Eich exercising, as thousands of others did, his first amendment rights in supporting the petition to Government (otherwise they would not have appointed him)...that they now have bowed to media and public pressure and have effectively punished (albeit not directly as Eich resigned, but their apology is engineered to forestall an ongoing PR issue) Eich for expressing his First Amendment rights..which is contrary to what Mozilla stand for. Admittedly Mozilla find themselves between a rock and a hard place and they either bow to public pressure about Eich's political support of Prop 8 which was inherently opposed to equality of marriage, or they disavow Eich for supporting such a proposition, which in turn infringes his rights...Like I said earlier, there are no winners here..Mozilla are effectively going against their very raison d'etre whatever position they take, for them the least painful route was the one offered to them by Eich himself when he resigned.
Besides, the reaction from the public wasn't about his right to say what he said (more accurately; support what he supported) - he is entitled to say it, and no-one (ok, not no-one, but it wasn't the thrust of the opposition) has claimed otherwise.
The problem was that his political position was in opposition to the implied values of the company he represents. Values which are part of the reason for customers choosing Mozilla's products over its competitors. It was a betrayal of values, and people were upset about it.
No, the problem was that Eich supported Prop8, that is it...it had nothing to do with what Mozilla represents (which is btw, nothing to do with LGBT rights, but internet freedom and freedom of information) and the the only reason Eich was forced to resign was because his private donation to the Proposition 8 campaign was publicly outed by Gay Activists. Eich was targeted by the media because he was head of Mozilla and designed Javascript (when he was CTO there was no such calls even though his donation was known at that time), not because Mozilla stood for Gay Rights or Equality of Marriage,
The Gay Activists targeted lots of people on that list, and not always legally either.
All Eich supported was a ballot that defined marriage as the union of a man and woman..a position shared by many people, including the United States current President I might add, should Obama resign because he stated he supported that definition in the past? I should think not...I find the whole intolerance of unpopular views by those demanding tolerance for their views as hypocrisy, for me the issue about the definition of Marriage is one for the constitutional policy makers and not one that should affect the individuals right to freely express and support their preference for one position or the other..what has happened to Eich is that one group (the aforementioned Gay Activists) have decided that his views are unpopular to them and that he should be punished for it (by effectively forcing Mozilla into a position where their business was at risk unless he stepped down). This I find to be in opposition of equality and contrary to basic rights of freedom of expression and conscience, not in favour of it as it is effectively blackmailing people into following a specific subjective morality and agenda at the expense of the individuals right to express themselves within the law.
For me that is what is wrong here, not that Mozilla asked for Eich's resignation, but the events that led up both Eich and Mozilla having no other choice.