Interesting article. Unfortunately Dawkins, who was once a truly marvellous writer on evolution, has developed a habit of handing down judgements on complex issues that rely more on rhetoric than reasoning.
I don’t know if you’re aware of his work in this different area, but at one point he wrote extensively in favour of atheism and against religion – a perfectly valid case to put, but it was painfully obvious that he was more interested in the demolition of “the other side” than in actually weighing up different arguments.
(He didn’t seem to realise, for example, that many of his objections to the existence of a god had been considered and countered by religious philosophers years ago. I am not religious, but one has to take intelligent arguments seriously, whoever they come from...especially if one is a professor at Oxford.)
The same applies here, I think. If someone genuinely wants to argue that chromosomally-determined sex somehow outweighs gender, or even that gender doesn’t exist independently of it, there is no reason they can’t explore that idea in a calm and open-minded way, acknowledging the counter-arguments too. But Twitter soundbites are not the medium for it, as you rightly point out...
His comparison with asserting a new race, meanwhile, is a distraction - almost a straw man. One could imagine race situations that are at least slightly analogous to trans ones (for example, where someone is adopted, is brought up as white and believes they are white, then one day discovers that in fact their birth parents were black), but in practice they must occur very rarely.
And if (because I think he could be hinting at this) he believes some people are “claiming” mistakenly or dishonestly to be trans when they are in fact not...well, that’s a different issue that has relatively little relevance to the situation of *actual* trans people. I'm sure it happens occasionally, as even the strangest things do, but there's no reason for it to become a major part of the conversation.
Incidentally - as a speaker of British English, I think your third bullet point on the definition of "courtesy" is absolutely right. Courtesy means that you are affording the person respect in a general sense, but not that you necessarily agree with them on the specific issue regarding which you are being courteous. It's more or less synonymous with "politeness". I do suspect, though, that Dawkins wasn't thinking long and hard about the implications of the word.