Belief in conciliar infallibility is flatly incompatible with Protestantism, because the latter belief-system holds that the Bible is the only infallible source of authority. Acceptance of conciliar infallibility is (to put it another way) inconsistent with sola Scriptura. But this is what the fathers believed.
I have used the example of the Jerusalem Council in several places in my apologetics, to argue for this very concept of conciliar infallibility, which (as you can see) is quite biblical; e.g., in my books: The Catholic Verses (pp. 7-11) and The One-Minute Apologist (pp. 4-5). See also my paper: The Jerusalem Council (Acts 15:6-30) vs. Sola Scriptura and James White.
You can read the entire passage from The One-Minute Apologist, courtesy of amazon's search capacity for the book: follow the search link; type "acts 15" in the search box, hit "go" and select page 4 from the results; then click on one of the arrows on the right of the page to access page 5.
Readers can also read the relevant passage from The Catholic Verses, by following the "search inside" link and again searching for "Acts 15" and selecting page 7, then following the right arrows for pages 8 and 9. By going back to the initial search results, separate access to pages 10 and 11 can also be had. By this method, full access to both passages is possible.
Now the eminent Protestant Church historian Philip Schaff confirms that this was the consensus belief of the Church fathers (though as a Protestant, he himself would disagree with this), in part based on the Acts 15 passage, which is what I have argued for years:
The authority of these [ecumenical] councils in the decision of all points of controversy was supreme and final.This is only the tip of the iceberg regarding the Church fathers' rejection of sola Scriptura. I've written tons about this, and my soon-to-be-published book on the "Catholic" views of the fathers will massively document this rejection.
Their doctrinal decisions were early invested with infallibility; the promises of the Lord respecting the indestructibleness of his church, his own perpetual presence with the ministry, and the guidance of the Spirit of truth, being applied in the full sense to those councils, as representing the whole church. After the example of the apostolic council, the usual formula for a decree was: Visum est Sprirtui Sancto et nobis. Constantine the Great, in a circular letter to the churches, styles the decrees of the Nicene council a divine command; a phrase, however, in reference to which the abuse of the word divine, in the language of the Byzantine despots, must not be forgotten. Athanasius says, with reference to the doctrine of the divinity of Christ: "What God has spoken by the council of Nice, abides forever." The council of Chalcedon pronounced the decrees of the Nicene fathers unalterable statutes, since God himself had spoken through them. The council of Ephesus, in the sentence of deposition against Nestorius, uses the formula: "The Lord Jesus Christ, whom he has blasphemed, determines through this most holy council." Pope Leo speaks of an "irretractabilis consensus" of the council of Chalcedon upon the doctrine of the person of Christ. Pope Gregory the Great even placed the first four councils, which refuted and destroyed respectively the heresies and impieties of Arius, Macedonius, Nestorius, and Eutyches, on a level with the four canonical Gospels. In like manner Justinian puts the dogmas of the first four councils on the same footing with the Holy Scriptures, and their canons by the side of laws of the realm.
(History of the Christian Church, Vol. III: Nicene and Post-Nicene Christianity: A.D. 311-600, Grand Rapids, MI: Eerdmans Publishing Company, 1974, from the revised fifth edition of 1910, 340-342; available online: see this particular portion online: § 65. The Synodical System. The Ecumenical Councils)
But despite the mountain of evidence, folks like the anti-Catholic polemicists David T. King and William Webster actually claim precisely the opposite: that the fathers supposedly accepted sola Scriptura en masse, as a matter of consensus. They argue this in their book, Holy Scripture: The Ground and Pillar of Our Faith, Volume III: The Writings of the Church Fathers Affirming the Reformation Principle of Sola Scriptura. I myself have seen King ludicrously state on some blog or discussion board (possibly James Swan's) that "all" of the Church fathers believed in sola Scriptura. How dense can someone be?
Don't fall for this constant revisionist history and anachronistic "proof"-texting. Anyone would do much better in accepting the scholarly word of Protestant historians like Schaff, Pelikan, Kelly, and Oberman, rather than the ignorant "arguments" of anti-Catholic zealots intent on disagreeing with the positions of Catholic apologetics, no matter how many historical facts and scholarly opinions get in their way.
One must, therefore, give high credit to one anti-Catholic Reformed apologist who bucked the trend: one "Saint and Sinner", who actually conceded this point. Perhaps he can convince his buddies King, Webster, White, Svendsen, Engwer (?) et al to follow suit. That would be a refreshing change.