People who don't like an argument for political reasons will attack its facts and reasoning whenever they see an opportunity to do so -- there is no XOR function here.

I never claimed there was, and its entirely irrelevant to the point. I only claimed that they will attack the facts (also, the facts are first on the list and often people stop right there because laziness edit: that's it, not xor but 'or else' aka the garden variety or that stops if first part is true). After they attacked the facts, if the facts are presented, there is a minor decrease to the weight assigned to the world model that has led them to attack the facts. No big effects are claimed. Just usually there is a zero decrease, and that can be significant difference.

Even if your premises are correct, a better response would be to take care to strengthen your reasoning and make your assumptions and definitions explicit.

Strengthening of reasoning is most necessary when you form the opinion. Very often by time people express their opinion, all they are strengthening is the justifications for already formed opinion, what ever that opinion might be.