She mentions the hypocritical rule in the GRA about hereditary peerages, and that there is now a transwoman hereditary peer in the HoL (but no actual women because they can't inherit a peerage), but she fails to mention the other side of this, that if a daughter of a hereditary peer transitioned, she still wouldn't be considered to be male for the purposes of inheriting her father's peerage.
So many good examples in that article though. If men are going to lose out, then nobody believes in gender woo, but if women lose out, who cares?