They are selling something. If you think a church is not a business, you are fooling yourself.
America is a nation of laws, not men. BB can and should pursue this trademark infringement, for the exact reason that their PR manager gave: "It's bad precedent to let some groups violate our trademark while pursuing others." If they allowed this God Squad vehicle to go unchallenged, what would happen then if the KKK tried to make a Sheet Squad vehicle?
You can dislike my comment into oblivion, but that does not change the fact that, in the US, NO ONE is above the law, not even Catholic priests. Given their recent history, perhaps I should say _especially_ Catholic priests.