Oh girl. If you think it's ridiculous (and it is, unless I've mistaken you and you're actually an incredibly precocious 12-year-old) then don't succumb to it. Yes, break-ups make people crazy, but as an objective third party, you do not have to "prove" anything about your loyalty. You prove you're a good friend by being a good friend, not by trying to control other people's friendships over of an expired boning clause. People get so territorial over people they used to regularly see naked. I've been asked to defriend others (both online and off) and it always struck me as bizarre. My Facebook friendship is like fruitcake -- I'm with you forever, baby! (Unless you do any of these things.)
Social media is, in a sense, a perfect medium for punishing people. It's less dramatic than keying someone's car. It's instantly gratifying, and it most likely won't land you in jail. (Possible exception: Courtney Love) But! It's also petty, and it reflects poorly on the punishers. No one wants to be the guy or gal who treats friends like the children of divorcees. Maybe such requests should be chalked up to temporary insanity and we should all just call it a day and go back making fun of Kanye West's tweets.
I do think there are some circumstances where it's reasonable to ask a friend to defriend an ex. For instance, if the ex was in any way abusive, or if he/she is using you as a middleman to gather information about your friend, or stalking the other person. Basically, if the ex is a serious douchecopter. Another reason to defriend is if you legitimately have no reason to stay connected, as in you never talk, never hang out, never plan to exploit them for personal and/or professional gain, and so on. If staying in touch with the ex in question is not important to you, then by all means, send them on their merry way.
What I would recommend as a compromise is that you take a brief hiatus from the amount of public communicating you do with this dude, which maybe isn't that frequent anyway, and therefore won't be a problem. If you're like, "Nooo, I NEED to regularly discuss the minor works of Kreayshawn with this guy on Facebook!" then at least keep your correspondences to private messages or texts -- stuff that's not visible to the world (and by the world, I mean your cray-cray friend). After a few months of keeping things on the DL, your ladyfriend will probably be over the Hump of Batshittery and you can all have a good laugh over those "dark months of uncertainty, angst, and Nutella-whiskey aperitifs."