This is an idea that grew out of my last post which spiraled into tessera hospitalis, tokens of friendship. It makes good sense that we have ones in the shape of joined hands. The dextrarum iunctio was a common symbol of concordia and fides. But what is up with all the half animals? I think that it is likely to represent the animal sacrificed in the creation of the union. I would also hypothesize that pigs are popular in this private domestic context for the same reason that we see pigs being used to seal a foedus.
Allow me to remind you of some famous numismatic pigs: