Come on, he didn't fund the war in Uganda. I don't share his views or anything but I don't see why "not liking the gays" or whatever should have any influence at all on whether or not he's suitable to run a tech company. It's not a political office.
The relevance to the CEO job is that he is a) boss of everybody at Mozilla, and b) the public face of Mozilla to customers, donors, partners, and the public. Having actively worked against the civil rights of gay people gives both groups cause to question their involvement, and has to make some employees nervous that they will face the same sort of discrimination at work that they have faced elsewhere in their lives.
Also, it's not about "not liking the gays". It's about things like letting gay partners have the same rights in medical cases of their spouses as straight spouses. It's about child custody, death benefits, and lots of other very important things that may not be a war in Uganda but they are massively important and life-changing for the people involved.
If a person in a position of power over others (hiring/firing/promoting) has openly held views of discrimination against a certain group of people, it is a problem. It doesn't matter if he's the president, or a CEO of a tech company.
Of course, its entirely possible that he doesn't let his views impact his work or the way he treats his employees.
For a long time, everybody was opposed, but now it's just fine with most people:
http://www.gallup.com/poll/163697/approve-marriage-blacks-wh...
Hardcore racists now know that talking about "miscegenation" will get them ostracized. So yeah, the KKK is a pretty reasonable parallel here.
It may not be "the war in Uganda", and it may not affect you personally, but it's certainly a critical issue for some people.