Of course there's a link. But criticizing an action someone has taken that happens to have been religiously motivated is not the same thing as objecting on principle to their religion.

An example more extreme than Brendan Eich's: Suppose someone is a devout Christian but also rather deranged, and believes that the Bible is full of coded messages telling him to kill (say) school biology teachers. So he goes and kills a bunch of school biology teachers. If I say "That was a terrible thing to do and he shouldn't have done it", that doesn't mean that I am going to hate on everyone else who is a devout Christian -- because, as it happens, plenty of people manage to be devout Christians without murdering biology teachers.

Perhaps (so far as I know this is pure speculation) Brendan Eich is a Christian and the particular variety of Christianity he adheres to tells him to try to stop same-sex couples' relationships being legally recognized. If so, then I think the particular variety of Christianity he adheres to is leading him to do harmful things and I wish he would stop. But that doesn't require me to object on principle to everyone who is a Christian, not least because plenty of people manage to be Christians without trying to stop same-sex couples' relationships being legally recognized.

Now, let us suppose there is a Christian denomination that has opposition to same-sex marriage as a central part of its teaching, and that does not permit anyone to belong to it unless they work to oppose same-sex marriage, including making financial contributions to campaigns like the one for Proposition 8. And suppose it turns out that some particular person is a member in good standing of that denomination. Then I'm quite happy following the following line of thought: This person belongs to that denomination; belonging to it means being a fervent opponent of same-sex marriage and contributing to campaigns against same-sex marriage; therefore this person has almost certainly done things I consider harmful and antisocial; so much the worse for this person. You may, if you please, consider this anti-religious bigotry. If so, I invite you to consider the following two questions. (1) Is it possible for a religion (or some particular version of a religion) to be morally harmful to its practitioners? (2) If you learned that someone was a member in good standing of an Islamic sect that had glorification of terrorism as a central doctrine, would you think worse of them as a result?