While I might take a similar stand against the hypothetical coffee shop, I believe your analogy misses an additional point. Opposing gay marriage is favoring discrimination against gay people. It's detrimental to the organization and the community for someone apparently prejudiced against gay people to lead Mozilla, which appears to be the case.

We'll see how the promised inclusivity efforts go. If he's genuinely committed to inclusivity, great! For the moment, however, I have reservations.