This is the opinion of Pope Saint Paul VI, expressed in his letter to archbishop Marcel Lefebvre in 1976.

“Nothing that was decreed in this Council, or in the reforms that we enacted in order to put the Council into effect, is opposed to what the 2,000 year-old tradition of the Church considers as fundamental and immutable. We are the guarantor of this, not in virtue of Our personal qualities but in virtue of the charge which the Lord has conferred upon Us as legitimate successor of Peter, and in virtue of the special assistance that He has promised to Us as well as to Peter: “I have prayed for you that your faith may not fail” (Lk. 22:32). The universal episcopate is guarantor with us of this.”

~ First, Pope Paul asserts that the Council and His subsequent decisions as Roman Pontiff are guarantees to be in harmony with the tradition of the Church — not because of the Pope’s personal qualities, but because of the charge given to the Pope, conferred upon him as the successor of Peter, just as the Church has always taught: the never failing faith of Peter and his successors.

“Again, you cannot appeal to the distinction between what is dogmatic and what is pastoral to accept certain texts of this Council and to refuse others. Indeed, not everything in the Council requires an assent of the same nature: only what is affirmed by definitive acts as an object of faith or as a truth related to faith requires an assent of faith. But the rest also forms part of the solemn magisterium of the Church to which each member of the faithful owes a confident acceptance and a sincere application.”

~ Pope Saint Paul rejects the idea that the Council’s teachings can be nullified or ignored by classifying them as pastoral (or non-infallible). And here is the stunning assertion: some of the things Vatican II taught are “affirmed by definitive acts”, and therefore require the full assent of faith due to formal dogmas. Then other teachings are non-infallible, and nevertheless are of the solemn ordinary Magisterium, which requires religious assent.

~ So Pope Saint Paul VI held that not everything in the Council was non-infallible! Some teachings were definitive and therefore require the assent of faith due to infallible teachings. Other teachings were non-infallible but still require acceptance and application.

Although Bellarmine and Ludwig Ott have asserted that everything taught by a general Council is infallible, I think we have to narrow that statement somewhat by attributing infallibility to whatever is taught definitively, and the rest would be non-infallible. Even so, most of what Vatican II teaches falls under this type of infallibility: LG 25, the teachings on Scripture and Tradition, the teachings on the authority of Bishops and Popes, the fundamental human right of freedom of religion, etc. Then decisions on discipline would largely be non-infallible, but still preserved from grave error.