This isn't about his "private beliefs", it's about his open funding for a hate campaign. The article is deliberately inflammatory, portraying this as being about a CEO's personal beliefs, but it's actually 100% about his actions.
CEOs are major figureheads, and their actions reflect on the businesses they run. You rule yourself out of qualification for certain jobs if you act in certain ways, such as actively supporting discrimination against many of the people you supposedly potentially lead.
And right now we have the usual suspects who've latched on to the fact that many people still hate gays as an excuse to bash homosexuals when they have the audacity to to stand up for themselves, who are proposing that this has something to do with this guy's personal beliefs.
If he'd donated money to a group proposing ending women's suffrage, we wouldn't be having this debate. The guy wouldn't be CEO.
If he'd donated money to a group proposing the re-institution of slavery for any black enfranchised as a consequence of the Civil War, we wouldn't be having this debate. The guy wouldn't be CEO.
But this is "OK", because he wants gays treated abusively?
No fucking way. If the Mozilla Foundation wants him to be a CTO, or a programmer, or a coffee maker, or a team leader, or a division head, or whatever, that's fine. But he's not suitable for the role of CEO. End of story. He's not qualified to lead.