Does this mean that a priori all practices of Source Criticism fall afoul of the Catholic Tradition? No. Why not? Because it is not inimical to the faith to suggest that this or that text from the bible has prior sources. Just see the opening remarks of the Gospel according to St. Luke.
But it does mean that we must study how its concrete practices are undertaken. We must take, one at a time, each iteration of the method calling for examination or evaluation. We can draw up a number of criteria.
Criterion 1: If the method presupposes genuine contradiction—where X and not-X are affirmed in the with respect to the same at the same time—in order to get off the ground, then it is fundamentally flawed; indeed, it is opposed to the faith. Consider our example from the creation accounts. If the critic supposes that these one account affirms X and the other, not-X, then his method is flawed at its roots. He is attributing contradiction to the two authors he will go on to infer. But everything that the human author affirms is affirmed by God (Dei Verbum; not to mention, the entire Tradition). Hence, God himself will be affirming a contradiction. This is an intolerable position.
Criterion 2: If the method presupposes that a purported announcement of the future is indication that in fact the author lived at the time of the announced event, the critic is temerarious. If the critic insists on the point, he must be presupposing the impossibility of someone having foreknowledge of the future. But (1) God has knowledge of all things, past present future. Indeed, this is de fide definita (Vatican I). And (2) Man is such that he can receive revelation from God (also de fide definita). Finally, (3) There is nothing repugnant to man receiving such a revelation of the future from God (This is the entire Tradition of the Church, not to mention the explicit teaching of Scripture). Hence, such a persistent critic is opposed to the faith. Example: Among the arguments for more than one author of Isaiah is the announcement of Cyrus as Messiah in Is 45. The lurking presupposition: “What man could possibly say, more than 100 years ahead of time, indeed close to 200 years, who some political figure would be, much less predict his character?” Ah. Examine that question. “Predict”? Predict is what hedge fund managers do. It is not what Almighty God does. God’s omniscience is not a reading of the future through immanent causes. Why not? Because there is no absolute determination of the future through immanent causes. This claim is true (a) because of freedom and (b) because of the non-absolute determinacy of physical causes. Solar eclipses and things can be predicted. But the total movement of the total set of matter in the universe cannot. But at any rate, let’s stick to basics. God sees the future he does not guess about it. He is not the great Weatherman! So, the entire question exhibits that the critic has ignored the fact that Almighty God is the primary author. The critic is so worried about “Dictation Inspiration Theory” that he runs off the cliff in the other direction. Dictation Inspiration Theory, writ global, opposes the humanity of the human author, since it denies that the human author uses his mind and creativity, etc., in writing. He is like a pure vessel, a mindless pen that scribbles God’s dictation. That theory is also opposed to the faith. But don’t run off the cliff in the opposite direction because the mystery of inspiration is difficult to fathom!
These are only some of the criteria. We could add many others.