I am gay and I think that for the company to be able to stand by their values and morals, one of which is declared as equality, the management of the company should reflect that not only in their professional lives, but their personal ones as well. It's the same idea that a CEO being caught in an extramarital affair reflects on a company and how he/she lives, operates, and performs in honest transactions (extramarital meaning that he/she took and oath to not be involved with another person). It's not to say that Eich should not have the right to believe in inequality, it's simply that his decisions reflect his, "state of mind."
While I understand that Mozilla holds freedom of speech dearly, I don't believe that you need to pick between one or the other. Just because Mozilla believes in freedom of speech and equality doesn't mean Eich can use freedom of speech as a platform to undermine equality -- that would be hypocritical and hopefully everyone can see that.