Dawkins probably wouldn't care too much about the women's rights angle, but he's a free speech proponent, isn't he?
Some of the "hate speech" / "no crime hate crime" stuff is dangerously close to heresy and blasphemy laws of old.
Also I would've thought he would care about children being told they were born in the wrong body, just because they play with the wrong toys, or have a feeling in their head, and need life long medication and surgery to "fix" it.