Were New Testament writers infallible when they wrote Scripture?

Inspired, Inerrant, Infallible

Let's be careful about the usual meaning of those 3 technical terms as they are generally used in Christianity, with different shades of meaning according to the different denominations, esp. between Catholics and Protestants. For a general overview, please consult the relevant wikipedia articles for Biblical inspiration, Biblical inerrancy, and Biblical infallibility.

For simplicity, this handout captures the general meaning succinctly:

1. Inspiration: about origin affecting the author: "From God"
2. Inerrancy: about the truthfulness of the text: "Without error"
3. Infallibility: about the authority on the reader: "Without fail"

Your question

Were New Testament writers infallible when they wrote Scripture, inspired through the Holy Spirit?

then contains a misnomer. While you are correct in using the terminology that the writers (the author) are inspired by God, it is incorrect to use the term "infallibility" to refer to the author, because in general use, "infallibility" means how the Bible produces the effect of being able to be received by the reader as authoritative teaching.

Illumination and the Holy Spirit

Now let's think how exactly the Bible can be infallible, especially when there are multiple interpretations?

Protestants have different answers than Catholics:

• For Protestants, who all hold sola scriptura, the effect of the Bible being authoritative (infallible) to the reader is due to the Holy Spirit illuminating the reader. In other words, the Bible's authority and enduring nature (i.e. infallibility) cannot be separated from the faithfulness of the Holy Spirit teaching the reader through the Bible. It's the Holy Spirit that leads the reader toward accepting what the Bible says as true teaching from God. That's why Protestants believe in private interpretation of Scripture because there is the Holy Spirit who teaches.
• For Catholics, they point to the evidence that Protestants interpret Bible differently so they question whether that's REAL infallibility. Instead they assign infallibility to the teaching office of the Church due to the Holy Spirit illuminating the Magisterium. While the Catholic church doesn't exclude the Holy Spirit illuminating individual Christians, the Catholic church teaches that when there is conflicting interpretations, the Magisterium is the one infallibly guided by the Holy Spirit.

Conclusion

Were the New Testament writers infallible when they wrote Scripture? Technically, No. They are inspired when they wrote Scripture. The Scripture becomes infallible when either the Holy Spirit or the Magisterium teaches the correct interpretation to individual believers. BUT for Catholics since the several New Testament writers were ALSO bishops (Magisterium), Catholics can say that they were infallible when they taught their own writings to the original audience, since their own writings that later became canonized are about faith and morals, the only kind of teachings that are deemed infallible.

Were they infallible when they do anything else? Protestants answer No, Catholics answer Yes, because there are some unwritten teachings of the apostles (about faith and morals, not skills as tentmaker, doctor, tax collector, carpenter, etc.) that were infallible to the original audience and were handed down through generations to become the Apostolic Tradition. The Apostolic Tradition becomes infallible to Catholics today as taught and interpreted by the Magisterium, similar to how Scripture becomes infallible to Catholics today through the same teaching office.

For Catholics, both the Scripture and the Apostolic Tradition form the single sacred deposit of faith that has been interpreted and transmitted infallibly by the Magisterium (the pope and the bishops) down through the ages until today.