But if you are checking if a person if qualified to be CEO, wouldn't their domain knowledge and ability to lead be better qualities to prioritize than their stance on gay marriage -- especially if their personal views have not been shown to affect how they intend to lead?
Absolutely. However, Eich's behavior after the donation came out revealed a crucial flaw in his ability to handle public relations. Even if this kerfluffle had been about something that isn't so contentious, it's been proven that he cannot handle criticism - something a CEO, the public face of a company, has as one of their primary job duties.
It also reveals a pretty massive conflict of interest wrt. his personal views on equality and Mozilla's views on equality. If it were any other corporation it may be different, but Mozilla's kind of famous for this.