I was in the middle of writing almost exactly what you wrote, but I scrapped it when I saw I'd just be redundant.
I would like to add onto your "reasonableness" point in that, just because someone can explain their views in a polite and reasonable manner does not automatically mean there's more legitimacy to their arguments. People see Rowling's essay on her views and think "well, that all looks reasonable, I can see how this was all just a big misunderstanding" but they either ignore, or are not well-versed enough on trans issues to notice, the falsehoods and inaccuracies she's spreading. Very intelligent people have always been able to politely and "rationally" explain all sorts of horrible ideas and if their opponents standing up for human decency end up shouting or getting angry, the audience thinks "Well, that's uncalled for. They probably don't have a good reason for their side if they can't be emotionless about it."
I try to be polite and reasonable whenever I discuss things, only because I'm aware of this tendency in people - but I also try not to completely shut out people's arguments when they're less in control of their emotions and yell or use strong language. Sometimes people have good reason to be angry and frustrated, they still need to be listened to.
It's why I kind of get annoyed when I see debates between two ardently opposed sides that end with "Well, I disagree with you, but I commend you for your ability to be calmly express your ideas. We may be on different sides but there's no reason we can't be civil." Meanwhile the debate was over the legitimacy of ethnic cleansing.