You’re taking an uncharitable interpretation of the comments you’re responding to, and I suspect that this might be part of the reason why the author of those bowed out of the conversation. And because of this, I think you haven’t really done your position justice at all, because you think they’re attacking your freedom of speech but really their argument is not that.

I think perhaps it might make a bit more sense if you replace “marriage rights” with something such as “right to life”, which might be easier to relate to. And to make it more even, let us replace Brendan Eich with one of those two-faced comic book serial killers who is a functioning successful part of society in the workplace but outside of it likes killing people. Nobody in particular, just people in general.

Now the question posed is, if you had no idea if they were a serial killer, would you work with them? The answer to that is “of course”: you know no reason not to. However, this issue is slightly different, because by some means it has been revealed that he is in fact a serial killer, but somehow this isn’t strictly illegal or anything so he’s coming in to work anyways. At work he’s great but once you leave work you are concerned (in general, not because he’s going to target you in particular) that he may be waiting in your bedroom to kill you.

Now we have a curious question of what we should do with this person. From a logical perspective, which is the one made in the comments you’re responding to, nothing should be done: removing him from his position doesn’t stop him from killing people, and if we do fire him we lose out on him entirely. I hope you can understand why someone might hold that position. And from that perspective, I think that they would likely respond to your letter with “you have every right to voice your criticisms, but I think you are being irrational because I cannot see how your letter asking Brendan Eich to be removed from his position helps your case because he can still privately donate all he wants regardless” (unless you in fact believe that he should not be able to hold employment at all and thus be unable to donate money because he is penniless.)

On your side, I think the argument is now fairly obvious: in the situation I described, I know very many people who would be hesitant to work with such an individual. We’re human, we associate qualities of a person and color all their actions through that lens. While you say you would be happy working with people of the opinions you mentioned that supposedly don’t directly affect you, I would strongly suspect it would affect how you thought of them at least subconsciously. Really, I think the opposition you have against working with someone who does not support LGBT rights is just this except amplified to the point where you can no longer try to correct your biases for that person because of it affecting you personally. And I think there is probably a very real negative effect of people working with others who privately hold views they don’t agree with, because that subconscious tension is always there even though if you look at it “rationally” it should have nothing to do with your work. And really, in many cases we seem to consider it OK to get rid of people who make everyone around them feel or perform worse.

Now, is that a valid reason to terminate someone? That’s exactly the argument here. Personally I tend to lean more towards “no” than most people would, I think. I am fortunate enough to not have anyone try to restrict my freedom of marriage or association to my knowledge, but I have worked with people who have never personally done anything to me but I have found out (usually after the fact, to be honest) that they hold fairly string views that I not only disagree with but I could consider attacking a category I might fit into (“people who defend freedom of speech of the alt-right should be punched”, “brown people are all H1Bs that take our jobs and we should send them back to their own country”). Notably, it was never an issue that I think I could measure impacting our working relationship, in many cases which I think I could prove for a fact because I didn’t know they held such views and they weren’t aware that I fit into the categories that they were talking about. And quite often I think we actually even did pretty well when we both were aware of this because it would just not come up in a working relationship. Would I work with them again? I think I would. I’ve come to realize that I personally have to separate people from their private (or private until solicited) opinions, because more often than not when I think I meet someone who shares my views on human rights they actually don’t and I’m just completely unaware. So for my own sanity I just have to separate them.