Ahem... Most of you are missing a part of this.
The article doesn't really make this clear -- but regardless of the official stance of Mozilla as a company, Eich himself has never actually recanted his opposition to same-sex marriage. He has promised not to discriminate against gay people within Mozilla, etc., but at no point -- as far as I have read, at least -- has he ever said that he has changed his mind, and that he is in favour of the right to equal marriage now.
If he did, I think -- despite what some of the commenters here are claiming -- that the attitude towards him would, indeed, change, and that his appointment as CEO wouldn't be seen so negatively. I think a lot of people who are upset about this would be perfectly happy with him staying on as CEO if he'd just make a public statement to the effect of "I was wrong, gay marriage is A-Ok, sorry about that." Maybe he could make a small donation to some pro-gay marriage cause, to "balance out" the donation he made for Proposition 8. I know that'd be good enough for me, anyway.
Also, I don't think that being for or against LGBT rights are just different flavours of political thought, as some commenters seem to be seeing it. Trying to pass a law to prevent gay couples from getting married isn't just advocating some harmless personal belief -- it's trying to force your personal beliefs onto others; in fact, it's being willing to hurt others in order to ensure that they comply with your personal beliefs.
Gay people don't hurt anyone when they get married. Advocating LGBT rights doesn't hurt anyone. Trying to take away gay people's rights, and trying to advocate for them, are not morally equivalent positions.
And free speech doesn't mean speech free from criticism, or free from consequences -- such as people no longer wanting to work with you. Eich is perfectly free to advocate against gay marriage. He's free to advocate against inter-racial marriage, for that matter, if he felt like it... But that doesn't mean he has a right to have everyone around him politely ignore his views, and carry on working with him like nothing in the world is wrong.
The only valid point I think I've heard so far in Eich's defence is that it's a reality of modern life that many of the products we use have morally-ambiguous origins -- obviously far more so than Mozilla, in most cases. That still doesn't mean any of us have to be OK with Eich, though.