You‘re right, it‘s always better to stay unemotional and matter-of-fact.
However, I remember some discussions on Facebook in which I just coudn‘t stay calm: Another intersex woman I know from Facebook had given an interview in the youth channel of Bavarian public TV, and some comments were so insulting that I identified them as fascist, incitement of the people and threatened to inform prosecution about it.
But as long as there is no insulting, matter-of-fact argumentation is the only way to make others possibly reconsidering their stance.