I looked over the Akiva Cohen dox, and I don't see where this guy has a leg to stand on legally.
On the grounds of him being relevant to a public discussion, he inserted himself into a conversation he could have stayed out of and thus the dox satisfies the curiosity of those wanted to know just who he was and why he was relevant, and all the information is presented as just that, information, there are no threats to his or anyone else's safety stated or implied.
Second, all the information was sourcable via means he made willingly public, and for the purposes of mockery, his public information was used for that purpose, and since comedy is protected and his information was posted with clear intent to derive amusement (and he proved the point with his subsequent freak out), and the case for parody looks solid to me.
Hosting his photos for purposes of commentary on them (as has been done with the information) would be a legitimate example of fair use.
He can still sue, but he's just wasting money tilting at a legal windmill, and all because he's mad he's being made fun of.