Do they still use horse parts for the glue that keeps the boxes shut?
(in reality there's almost no chance, synthetic glues are way easier to manufacture and manage, outside of gelatin animal glues would near-only be used for restoration or specialty applications e.g. some lutherie and other speciality woodworking)
Of course this conversation also ignores the fact that fining agents are removed from wine before bottling as part of their purpose - they bind with the crap you don't want in your wine. Typical store-bought wine will have no detectable amount of a fining agent in it.