boycotts
Yep, totally within your rights to boycott someone for whatever reason you like. I would still disagree with that being a good reason to boycott, though.
Absolute worst case scenario is that the CEO's policy and business strategy is having a negative impact on the greater society. So that would be a weapons company encouraging a huge military budget through lobbying, or something. Most companies don't have that kind of impact, so more likely the worst case is limited to internal culture of the company and whatever ways the company can influence its employees through its management methods. That's even if you're saying the CEO is manifesting their beliefs in their work, which is certainly not something you can assume. I don't think there's any evidence of Mozilla, the company, actually engaging in homophobic practices. Some would say the worst would be the company making donations to a political organization, but that actually needs the board of directors to be involved.
As for the freedom to 'look down on people', I don't have a response for that kind an attitude, and am not sure what you want intend to actually change by calling people idiots (to say this guy is an idiot would be ridiculous, as LW pointed out earlier I think).
The actual character of a person absolutely has a bearing on their business. Absolutely. It's completely out of touch with reality to say that a persons personality and beliefs don't have an actual impact on what they do or say.
Really I think if this man was a racist instead I don't think anyone would be having this discussion, but somehow taking action against same sex couples isn't considered discrimination yet.
Key issue here is the use of the phrase 'their business'. They're a manager, whose scope is generally limited to the internal day to day functioning of the company, and whose only obligation is to the shareholders. Again, I don't think there's any evidence of Mozilla engaging in homophobic practices. There are cases where the CEO takes on being the face of a company as a marketing strategy, like Apple and Steve Jobs, but that's still just marketing.