He was promoted from inside the company, and they feel that he shouldn't have been.
If he was promoted from inside the company it was because of his job performance. His detractors oppose him because of something he did that wasn't work related, on his own time.
Oh, and if you don't want your political contributions to become a big deal in the workplace, I have a couple recommendations: ... The policies of a new CEO are assumed, with reason, to be the intended policies of the company.
That is BS. The political contribution he made were personal, unrelated to the company. Nobody could reasonably confuse the two - his personal contributions and what the company policy was. If he had Mozilla make contributions as a corporate entity that is a different question.
A few thousand dollars publicly and visibly donated to a very controversial, discriminatory cause? Well, that's going to grab some attention. It still won't make headlines though, unless people have reason to believe you're in a position to discriminate against others going forward. See #1...
In other words, people should only contribute to the causes that you personally approve of. Besides that, company officers aren't government officials.
If you really want that to stick that could be bad news for a lot of companies. Apple, for example, has a gay CEO. Should Apple then be boycotted?