None of the Corleones were devout or practicing Catholics, despite attending church on special occasions or adhering to certain rituals when convenient. They weren't different from many (most?) other Catholics (or Protestants or Jews, for that matter) in that regard.

But "religion" played an important role in all three films, in a deeply cynical way. Notice how violence invariably gets mixed in with religious ceremony or occasions throughout the Trilogy. Vito gets shot right around Christmas, with all the yuletide trappings blaring at us in that scene and the surrounding ones. The Great Massacre of 1955 occurs against a backdrop of a baptism, with church music. The massacre climaxes as the priest asks Michael, "Do you renounce Satan and all his works," and Michael says "I do." And: Fanucci murdered during the San Rocco religious parade, the Tahoe machine-gunning following Anthony's first communion party, Fredo murdered while saying his Hail Marys, Archbishop Gilday's corruption, Zasa murdered during the San Gennaro Festival--you know all the rest. You don't have to be a Certified Deep Thinker to figure out what FFC is trying to tell us.