In an earlier post, I offered some thoughts on justification by faith in conversation with a Catholic theologian. What often arises from this line of inquiry is the question of whether or not, in light of the Catholic Church’s denial of justification by faith (preferring by faith + works of love), she is in fact an apostate and thus false church. In what follows I will offer a nuanced answer which does not completely avoid the tensions intrinsic to the question.
On the one hand, the Catholic Church has been faithful to maintain orthodox Trinitarianism and Christology. Without these, there is no church. Because the Catholic Church has been faithful to do so, the object of our faith, namely, Christ, and in turn the Triune God has been preserved, which means that people can have a real, living faith in the Catholic Church.
The height of heresy is to lapse into a denial of orthodox Trinitarianism and Christology, though I am willing to grant that the communions which did not fully embrace Chalcedon in the East, such as the Ethiopian or Armenian Coptic, may be in substance orthodox but be uncertain of the sophisticated promulgation of Christology found at Chalcedon. Therefore, inasmuch as the Catholic Church clearly presents the object of our faith—to the Father, in the Son, by the Holy Spirit—then she is a faithful part of the body of Christ.
But, her seven sacraments, her understanding of purgatory and indulgences, her understanding of the institutional church (e.g., the conflation of the church with the kingdom of God; pope as vicar of Christ) and her soteriology (denial of justification by faith; collapsing of justification into sanctification) to different degrees obfuscate Christ as the object indeed the founder of our faith. So, in that regard, there are heretical elements within Catholicism.
Now, before the pro-Catholic reader throws up their hands in disgust, know that inasmuch as any tradition or church culture does this, they are in disobedience to the head and husband of the church. So, there is potential for heresy in every tradition (and, in turn, every church) hence the phrase semper reformanda. But, the difference between these traditions or congregations and the Catholic Church is that they are not official documents that carry the weight that one finds in Catholicism nor are they capable of same breadth of influence as no Protestant tradition approximates the same degree of hierarchical authority as is found in the Catholic church (not even the Eastern Orthodox are as unified in their hierarchy as they lack a person with the same authority as the pope).
To clarify then I would argue that there is an element of heresy build into the very nature of Catholicism as it resists and actually prevents reform to the degree that would clear away those elements essential to it which obscure a clear faith in Christ. Moreover, if we take justification by faith alone to be supported by Paul, then we would also have to affirm his anathema spoken to those who deny it (Gal 1). This is a serious thing, one not to be stated lightly. One must ask: should the apostolic word of curse be granted authority against those who deny or obscure justification by faith? Francis Turretin summarizes well what I am attempting to communicate:
The Church of Rome can be regarded under a twofold view (schesei); either as it is Christian, with regard to the profession of Christianity and of Gospel truth which it retains; or Papal, with regard to subjection to the pope, and corruptions and capital errors (in faith as well as morals) which she has mingled with and built upon those truths besides and contrary to the Word of God. We can speak of it in different ways. In the former respect, we do not deny that there is some truth in it; but in the latter (under which it is regarded here) we deny it can be called Christian and Apostolic, but Antichristian and Apostate.
Now, I hasten to add that we are not justified by intellectual assent to justification by faith alone (cf. James 2:19), we are justified by faith in Jesus Christ, in whom alone we find access to God. So, I do believe that for those Catholics that keep the object of their faith, Christ, always in view (speaking with more rhetoric flourish here rather than precise phrasing), they are in fact true Christians; that is, in spite of not because of key doctrines of Catholicism which obscure this faith.
There is a cognitive dissonance that I am willing to grant to all believers; that is to say, despite intellectual affirmations that are unbiblical or even endemic to the Christian faith, it is possible to have saving faith, at least in the case of Catholics (not, e.g., Mormons or Jehovah Witnesses). I greatly benefit from and enjoy reading Catholic theologians, especially when they are thinking on Christ or the Trinity. The Catholic theologian Doug Farrow with whom I engaged in the aforementioned post was more difficult because he was directly arguing against what the Bible teaches, at least at points. Yet, he was also encouraging because he was willing to challenge some of the trappings of Catholic dogma (esp. Thomism), which in many ways served to move those dogmas closer to the truth of things.
So, to summarize, I am not willing to grant, contra my more extreme Reformed brethren, that the Catholic Church is apostate in toto. I do think there are some heretical elements found within her, and many of these are officially promulgated, but the orthodox teaching on The Trinity and Christ is also maintained allowing for true Christian faith within her ranks. Though I wish she would allow the kind of reform that is necessary to clear away some of the dross. I pray also that all churches, whether large or small, whether hierarchical or congregational, would allow the ascended Christ, by his Holy Spirit, to continue to convict and transform, conforming his Bride to his image (Rom 8:29) so that she may be a bride without spot or blemish (Eph 5).
 Institutes of Elenctic Theology (Phillipsburg, NJ: P&R Pub., 1997), 3:121.