I think it is more than just having one's sanity questioned. Speaking for myself, I react this way not because I don't value rationality over what feels good, but its that it seems there is knowledge behind my belief and I'm being forced to reject it because I am not articulate enough to defend it. This can be a major problem if the cultural context of the debate does not contain the right words and concepts to explain what I believe. Consequently, since debates go to the most succinct and clear, I must lose, but not due to necessarily having a more irrational belief. Then, if I persist in my belief, I become ostracized as an irrational person.
Articles like this merely fuel the feeling of impotence in the culturally disadvantaged like myself, leading to a more irrational defense of their (my) beliefs, and a vicious cycle follows. This is the "core going critical" that pg mentions. The ultimate result will be a more "rational" person, but they are more "rational" because they have been lobotimized.
I look at politics and religion as deeply personal choices. I also think they are somewhat "beyond reason" -- I don't want to use the term irrational because my point is that the rules of rationality don't apply. Perhaps trans-rational? And when I mean religion, I include the atheists here. They're as impervious to reason as any of the others, but mostly can't see it, which makes them a bit humorous to deal with.
The problem is that most folks are 1) very uncomfortable with this situation, and 2) can't find the words to express the "why" of what they are saying (except for the rationalists, who will use reason ad infinitum regardless of which side of the issue they stand)
I think the most honest responses are, like yours, where you say that there's good reasons that you just can't get to. I also respect people who say "beats me" -- the agnostics. I'm more of an agnostic these days when it comes to religion, and for a long time I've realized that politics is completely non-rational.
That's not to say you can't use logic and reason in the discussion: I think they provide tools to meet in the middle and share equally. But logic in these discussions has a completely different purpose than it does in say, a geometric proof. It's a flashlight in a dark, constantly changing room. It's not the light switch. Most people miss that point.
I enjoy seeing people talk about religion and politics (as long as it's civil) because it gives me an idea of how they think. It's neat to watch people struggle with really tough questions. Who knows? There might be something I could learn there. But I can see where it can destroy a forum.
Articles like this merely fuel the feeling of impotence in the culturally disadvantaged like myself, leading to a more irrational defense of their (my) beliefs, and a vicious cycle follows. This is the "core going critical" that pg mentions. The ultimate result will be a more "rational" person, but they are more "rational" because they have been lobotimized.