... I automatically should've been equally "tolerant" of (that is, refrain from objecting to) the actions of the bigots...
Not refrain from objecting to his actions, refrain from objecting to his being a CEO of a tech company. All these objections about his views and how they relate to his qualification as CEO would be completely valid if he were a CEO of an organization that advocated for gay rights, but there's nothing inherent in what Mozilla does that necessitates a different viewpoint. It's like saying "someone who believes in Palestinian statehood shouldn't be CEO of a tech company that employs Jews" or "someone who opposes abortion shouldn't be CEO of a tech company that employs women who may have had an abortion." My point is it's not relevant.
They deserve the same rights & respect that I have simply by default -- including being able to go to work without having a leader that tried to make them second-class citizens.
It should be obvious to everyone that the supporters of Prop 8 don't see it this way, because they don't see "gay marriage" as the same thing as "marriage". They don't recognize it as a form of an existing right, but a different and newly claimed right, that the state shouldn't recognize due to the nature of marriage and the state's role in protecting and promoting that institution. The crux of the issue is whether it's a right or not, and the side advocating for it hasn't demonstrated to the other side why it is. People that supported Prop 8 aren't necessarily bigots, homophobes, or any of the nasty labels that get tossed around so much (although I'm sure many of them were).
For an analogy to interracial marriage: if you believe it's bad because members of race X are inherently of less worth, then you're racist. If you believe it's bad because for some other reason it would be detrimental to society, you aren't necessarily racist. In the case of interracial marriage, though, there's nothing about race that's relevant to the institution, even as it was practiced in segregated regions. Sex, however, is relevant to marriage; this is why I think the comparisons to the civil rights crusade of the '60s are not apt - serious opponents of Prop 8 aren't really claiming that gay people are "less human." I'm a little too young to have been around during the civil rights era, though, so if anyone knows of arguments made during that time that are more applicable I'm open to correction.
(Wanting to do it, or believing it should be the case, is one thing; actively trying to make it happen seems a whole lot more hostile.)
It shouldn't seem more hostile - if someone has an opinion on how some aspect of society should function, I expect them to advocate publicly for that position, be they the Klan, neo-Nazis, NAMBLA, Christians, the "gay lobby", or anyone else. It's not somehow "worse" for someone to try to enact the social changes they think should be made.