With 1.1 I've seen a stack of Papal troops try go grab rebel settlements up in france (Florence was taken).

And no, I do not want the Papacy to be active, as in building armies and taking over lands. Perhaps they could "request" you return Jerusalem to his excellency, but having an AI faction with the dodgy attack/blockade code for triggering wars lumbering around with insta-ban.. no thanks. Never seen it naval invade, but it does have a little fleet to chase pirates.