Reformation and the Early Church Fathers

In the comments to this post, an anonymous Catholic claimed that the early church fathers "are by and large Catholic," and that may be true in terms of some visible, external practices (i.e., "making the sign of the cross"), but in truth, the current Roman Catholic religion (doctrinally) is, in the words of one of the other posters there, "nowhere to be found."

This is not a novel claim. In fact, John Calvin made the exact claim in 1536, in his "Prefatory Remarks to King Francis," delivered with the very first edition of Institutes in 1536:

Misleading Claim that the Church Fathers Oppose the Reformation Teaching
Moreover, they [our Catholic adversaries] unjustly set the ancient fathers against us (I mean the ancient writers of a better age of the church) as if in them they had supporters of their own impiety. If the contest were to be determined by patristic authority, the tide of victory – to put it very modestly – would turn to our side. Now, these fathers have written many wise and excellent things. Still, what commonly happens to men has befallen them too, in some instances. For these so-called pious children of theirs, with all their sharpness of wit and judgment and spirit, worship only the faults and errors of the fathers. The good things that these fathers have written they either do not notice, or misrepresent or pervert. Then with a frightful to-do, they overwhelm us as despisers and adversaries of the fathers! But we do not despise them; in fact, if it were to our present purpose, I could with no trouble at all prove that the greater part of what we are saying today meets their approval. Yet we are so versed in their writings as to remember always that all things are ours [1 Cor. 3:21-22], to serve us, not to lord it over us [Luke 22:24-25], and that we all belong to the one Christ [1 Cor. 3:23], whom we must obey in all things without exception [cf. Col. 3:20].