Yet, we are forcing everyone to take a stand on this "moral" issue.
He can either support Bills of Rights, against Bills of Rights, or he can do nothing about it, in which case is pretty much in the same camp as the opposition. The only difference is he chose to not care and yet he will probably be judged for not helping human rights. And human rights, to many is a worthwhile ethic cause. Not an individual morality debate; just as gay advocates would think gay rights is a basic right of human. If Brendan chose to say "I have no opinion" he is neither against nor supporting gay rights but his decision will disappoint the gay advocates in which case the advocates will not be happy with Mozilla. Therefore, everyone has to take a stand even if it were "I don't have any opinion."
There is a limited prohibition against screening for political affiliations enforced by the Federal government when filling certain civil service positions, but that's about it.
For a good summary of what types of discrimination can and cannot trigger legal liability, see here:
Of course it isn't.
If he was backdooring JS crypto libraries for the NSA, or shooting orphans, or selling crack, that would be seriously inappropriate behaviour and he would lose his job for it.
Many people might consider it inappropriate to be fighting against gay marriage - it's not just a political issue, it's a moral one.