“Thus, one Protestant may affirm, as do the English Puseyites the truth of all the doctrines underlying the Mass – the Real Presence, the Sacrifrice, the sacerdotal power of consecration, etc. – another Protestant may affirm that all such conceptions are false, yet both these Protestants are Protestant because they communicate in the fundamental conception that the Church is not a visible, definable and united personality, that there is no central infallible authority, and that therefore each is free to choose his own set of doctrines.”

– Hillaire Belloc The Great Heresies

I think this is where Anglo-Catholics differ even with the Eastern Orthodox. The Anglo-Catholic will exist side by side with the Anglican Zwinglian and the Anglican Calvinist, because he truly does not recognize “the Church” in the same theological way that Catholics or Orthodox understand her, i.e. “a united personality,” to use Belloc’s words.