But they probally have some extreme high security vault in case of nuclear war (especially due to the cold war) to hide the pope and what not with bibles and stuff like that
Vatican City is rumoured to have some sort of Fallout shelter and it would be much more than Bibles that survived. The Vatican Archives as far as I know is a fortified underground bunker built to withstand intense bombing and destruction.
Assuming it survived, it would be one of the most
if not the most complete source of art, history, and european culture in the wasteland.
The Vatican Museum holds a lot of art depicting Roman gods so those scavengers may get some conflicting informatiom
From what we've seen from Point Lookout, there hasn't been anything to indicate that the belief system has changed much at all. Marcella mentions "breaking bread" with Father Clifford, there is still restrictions on clerical celebacy (aka Diego), Marcella perfoms a last act of contrition, and she mentions that the Abbey of the Road gathers religous artifacts.
And like I said, St. Monica being a new saint indiciates that there is still canonization occuring.