Baby Jesus thieves literally take the Christ out of Christmas. When they do, it becomes apparent that the sacred object is also a piece of property, protected by the law that protects property and this whole apparatus that defends Christmas: fences and lights, tracking devices and private security companies, patrolling police and the courts. The commercialization of Christmas is visible here in a way it might not be, otherwise. That's the power of the joke.
Stealing the baby Jesus can seen as a protest against the commercialization of Christmas, which is to say against Christmas, since the theft, as a theft, shows how indistinguishable the commercial and religious aspects of this American holiday really are.
Read the rest of the essay, Thieves Taking the Christ out of Christmas. Literally., at Religion Dispatches.