Ah damn. I thought that was a joke, but according to Papal law it does indeed appear they have some claim on the Moon, though it is unclear who specifically has overlordship of it.
HOWEVER, since it is technically Christian to the church, if it was settled by those of another belief, it could very well have a crusade called upon it, no? Is that not the inception of the Crusades?
Nope. The First Crusade was requested by the Roman Emperor Alexios I Komnenos who wanted to repel the Turkish encroachment on Anatolia. Urban II acquiesced the request, through the Council of Clermont, and made the conquest of Jerusalem a secondary goal. That goal soon evolved to be the primary goal.
The Crusade itself was split into two parts: the People's Crusade, that made its way across Europe, massacring Jews along the way, until reaching Anatolia where they were utterly defeated by the Seljuk Turks; and the Princes' Crusade, the official one, that captured Nicea in 1097, Antioch in 1098 (and conducted a massacre of Jews and Muslims there) and finally Jerusalem in 1099 (again killing a bunch of Jews and Muslims). Most of the conquered territories were given to the Latin crusader realms, namely the Principality of Antioch and the County of Edessa. This caused attrition with the Roman Empire, who wanted the Levant returned to them. Of course, most crusaders treated the war as a pilgrimage and soon returne home to Europe, leaving the region poorly-defended and thus giving way to muslim retaliation and the following crusades.