We've all seen protest signs in the format [good thing] not [bad thing]! We also know that activist groups tend to be fractious, with splinter groups objecting to the main group's framing of the issue. In this game, you'll play improbable activists coming up with clever protest slogans.
Using a radically non-hierarchical democratic process, pick a starting player. That player should declare "I'm a [cause] activist. [A] not Bombs!" Another player should then jump in and declare "Well, I'm a [different cause] activist. [B] not [A]!" A third player would then say "well, I'm a [yet another cause] activist. [C] not [B]!" The causes for which you are activists can be as ridiculous and fanciful as you like, and the slogans are likely to become increasingly absurd as the game progresses.
The most important rule is that the two items in the slogan must either alliterate or rhyme. So the first player could be (among other things) a facial hair activist chanting "Beards not Bombs," or a mothers' rights activist chanting "Moms not Bombs." Alliteration should alternate with rhyming -- so the second slogan could be an eccentrics' rights activist ("Weirds not Beards!") or a pro-condiment activist ("Mustard not Moms").
There is no winner in this game -- just play until you get tired of it.