You raise an interesting objection. Some questions in this regard:
1) What does inclusivity have to do with Mozilla's core business, namely open-source Internet software?
2) Can any organization declare inclusivity as one of its core values and start enforcing it by firing every person in position of power who holds an exclusionary view on any subject? By the way, there are more people in positions of power than just the CEO. Every person in the corporate hierarchy, except perhaps the lowest, holds power over other people. The exact same argument you make about the CEO can be made about a VP, a CTO or a teamleader. They all represent their group in front of everyone else and they are all looked up to by their inferiors.
3) What is an exclusionary view? Is it one advocating that people in certain category deserve less than in another category? But by that logic, you hold an exclusionary view: after all, you support the idea that people with particular views should not occupy positions of power.
4) Why is it a good idea for an organization to declare holding exclusionary opinions a punishable offense? I can tell you why it is a bad idea. Quoting an excellent comment [1] below, "there's something wrong with injecting ideology into everything, that is, dividing everything in the world into what supports your ideology and what doesn't, making all judgments based on it, and shunning all who don't share your ideology. All must prove their purity and loyalty or be excommunicated. It's a very dangerous approach, and a quick glance at history books will tell you what's at the end of this path."
The life is a complex, non-binary (in fact, multidimensional) thing, and we all err in some regard, including yourself. You don't want to be discriminated based on your opinions, unless you overstep the boundaries of law.
[1] https://news.ycombinator.com/item?id=15398460