I think a lot of men will just look at GLs tweets and think "why do you care?"
They do - recently someone who seemed to know him was trying to get him to back off - basically asking him why he cared, it wasn't his fight. Mr. Linehan (sorry, I just can't use first names, formal childhood) was clear that he has daughters (and a brain in his head), and so it was his fight and no, he wouldn't back down.
As to how to get men engaged, I think that ManFriday at the Hampstead ponds demonstrated that men value their privacy as much as women - I think that this kind of direct action is the best way to get it across to reasonable people (Whereas the angle that it's letting AGPs in to change with your girl children just brings out the vigilante sort of man I would suspect)