If your belief is that you want to deny rights to some people, you are going to be held accountable by society in the sense that you won't get to hold powerful jobs. You won't be arrested, but society isn't going to let you run a public company.
What does that are liberals who are trying to assert their power. Now I would bet that most of the liberals who helped bring about that result wouldn't support a legal right for polygamy, polyandry, or marriage between close relatives.
Why not? While being sexually attracted to close relatives is very rare, the portion of the population that is preferentially polyamorous is larger than the proportion that is preferentially gay. Why should people who wish to make multiple commitments not have the rights that gay people have?
I submit that their reasons for not supporting those causes are no better or worse than Brendan Eich's for not supporting gay marriage. I further submit that when people are punished for publicly supporting statements that half of the nation supports, you're creating chilling effects for free speech that fly in the face of how this democracy is supposed to work.
In the sake of disclosure, my white mother was married to a Chinese man before that was legal in much of the country. Furthermore my sister performed a gay marriage before THAT was legal most places, and I have another close relative who was openly polyandrous for over a decade. As a libertarian, my only issue with gay marriage is why the government involves itself in people's private affairs.
But that is a lot less important to me than concern over political correctness making people feel scared about expressing unpopular opinions. When am I going to have an unpopular opinion that I get penalized for?
And your presentation of his belief is, again, very uncharitable. A decent percentage of conservatives were in favor of civil unions and other legal work arounds to give gay couples the same benefits as straight ones. Many didn't really care what gay people did and were just afraid of the slippery slope.