If Eich were opposed to net neutrality, or against open internet standards, etc, those would be damning beliefs for someone in the Mozilla CEO spot. Gay rights, however, have nothing whatsoever to do with Mozilla. (I agree with you that Hobby Lobby would fire a pro-gay-rights CEO, but we probably shouldn't be taking lessons on reasonable behavior from Hobby Lobby.)
If Mozilla does represent any kind of broad social alignment, I would hope that it would be one in favor of diversity of opinion and free speech.