As several noted in the comments, Catholicism has already split. Catholicism is actually not one structurally unified body --- and hasn't been since 1054. The Orthodox churches are Catholic, the biggest headed by the Patriarch of Constantinople. The Anglican Communion (including the U.S. Episcopal Church) identifies as both Catholic and Protestant, headed by the Archbishop of Canterbury. The old Catholic churches of Europe formed in the late 19th century as harbor for Catholics who rejected papal infallibility; they are in communion with Anglicanism.
In the United States at least 200 separate small Catholic churches and clergy associations exist, often with their own bishops. Some are CORPUS, a corps of married priests who celebrate the sacraments; Roman Catholic Womenpriests, who like many others are ordaining women; and the Ecumenical Catholic Communion, which has partnered with the other two groups.
Third, flows. Some people live in several Catholic worlds. In the United States, a Catholic woman might attend a Roman parish, work for Catholic Charities, serve as an independent Catholic priest, officiate weddings for divorced Romans on weekends and do Buddhist meditation every morning, too.
What would it mean to account for vernacular Catholicism? Non-Catholics? Flows between Rome and other institutions?
Understanding one of the world's most populous faiths needs to encompass all of Catholicism - -not just the Roman version.
And certainly not just the pope.
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