It makes solid sense for a company to choose a leader, the person who sets the tone and communicates to the public, partners, and stakeholders for it, who reflects the values of the organization and its stakeholders.
Mozilla stands, among other things, for freedom both online and off.
Eich certainly has technical chops, and has contributed, technically, to both Mozilla and the Web. There's no doubt about that.
His personal values, as reflected through his public political actions, were an extremely poor fit. In his prior role as CTO this wasn't as significant an issue (though it could likely have emerged eventually). As CEO there's simply no question that they were polarizing and distracting to the extreme. Especially in light of how he addressed the controversy once it emerged.
Quite bluntly: he wasn't up for the job.
I'm not saying this as a GLTBQ individual, or someone with an unblemished record myself on this (attitudes have changed tremendously over the several decades I've been aware that alternative sexual orientation is a thing) or other issues. It's a reflection of contemporary moral values -- and I absolutely believe that there's a large room for movement in such values.
If you want to reflect on that for a while, I'd recommend James Burke's The Day the Universe Changed, which addresses beliefs. The first and last programmes in the series address this particularly episodes 1 and 10, which reflect specifically on how beliefs have changed over time.
http://en.wikipedia.org/wiki/The_Day_the_Universe_Changed
If nothing else, this is a mark of just how far we've gone from beating up faggots for lols (not that this doesn't still happen) -- even under cover of law (Stonewall and similar events), if not without sanction or consequence for those so engaged.
For those who are suggesting that Eich was singled out where others more deserving haven't been: Mozilla proved itself to be more susceptible and responsive to moral suasion and pressure. There are plenty of companies (and other organizations) exhibiting poor moral character: Dropbox's appointment of someone widely regarded as a war criminal to its board, ongoing boycotts against Chick-fil-A, growing actions against the Koch brothers and the industrial and political network they control, campaigns I recall against Nestle, Carl's Jr., grape growers, and other causes.
The fact is that moral and market pressures can work, and in a world in which enterprises far too often disclaim all but the smallest shreds of moral responsibility, they're often one of the few effective tools available.
So while I do feel a slight bit of sympathy toward Eich (he was caught up in changing times), I applaud the action and result.