And what if he did? Does that strip him of his rights?
Depends on what rights you are referring to. There is no absolute right to anonymity in public statements. Individuals do have a right to free speech. CNN knows, or should know, that outing the meme guy’s identity will bring down violence against him, his family, and property by Leftist goons. CNN is using that mechanism to violate his right to free speech unless he tows CNN’s party line. If CNN outs him, and others inspired by the chum CNN has amply spread on the waters, harm the person, then CNN is civilly and criminally liable for the results, for what that’s worth after he’s ben lynched.
On a personal level, if someone is sufficiently loathsome, and actually engages in online speech that promotes hatred and violence against others (child molesters, Nazis, terrorist jihadis, etc.), I might not care very much if CNN ruins them. All that is subjective. My question is really: Is CNN mischaracterizing the man’s past statements to demonize their opponent and fire up violent people to go after him? Given CNN’s habits, I suspect they are.