I feel that RD has lost his way, and is trading upon his status as academic celebrity rather than engaging with the century long academic debate. I'm going to cover just the first paragraph of his argument, "Sex is not the same as gender…" to illustrate.
This will undoubtedly upset people, but as ever Dawkins excels at using words carefully to express his thoughts.
For me, though, it misses the most significant point:
If we did not treat and judge people differently depending on their gender none of these problems would exist.