It sounds like this guy is a real piece of shit. You don't say how many sessions you've actually had with him. I would assume that either he knows that his views are unpopular, or you've managed to avoid gamer politics since he joined up, since you didn't know about his toxic bullshit until you became FB friends with him. If you have any female players in your group (or LGBT players, or whatever else he rails against), you should definitely have a conversation with them about his beliefs and their comfort level having him at the table.



If they are okay with giving him a chance, then let him stay, so long as he behaves himself. If he doesn't bring up his beliefs, and acts courteously toward everyone, then he's not a problem. If he acts up, give him a warning (if it's something mild), or just drop him like a stone. You have a responsibility toward making sure all your players are comfortable, not just him.



The only way to defeat a Gamergater is through persuasion. If you can provide him with a positive example, and maybe figure out why he's so threatened by women in gaming, you may be able to help him move past his bigotry. No ally is stronger than one who used to be on the other side. Of course, that is a tall order, and if you don't feel like putting forth that amount of effort, don't. You aren't responsible for saving the idiot from himself.