Is there any support in Vatican II for such a conception? Is acceptance on the part of the faithful limited to solemnly defined teachings, clearly infallible for that reason? The Second Vatican Council also answers this question clearly and forcefully:

This loyal submission of the will and intellect must be given in a special way to the authentic teaching authority of the Roman Pontiff, even when he does not speak ex cathedra, in such wise, indeed, that his supreme teaching authority be acknowledged with respect, and that one sincerely adhere to the decisions made by him, conformably with his manifest mind and intention, which is made known principally either by the character of the documents in question, or by the frequency with which. a certain doctrine is proposed, or by the manner in which the doctrine is formulated.

Unfortunately, some theologians, particularly moral theologians, for reasons we will examine in subsequent chapters, have simply rejected this clear teaching of Vatican II. They have come to see their role as one of criticizing, passing judgment on, and even dismissing magisterial teaching.

There is no surer protection against this attempted usurpation than the documents of Vatican II themselves and particularly the passage just quoted from the Dogmatic Constitution on the Church (Lumen Gentium).

There is, of course, something odd in the effort to quarrel with what are obviously teachings of the Church and therefore require religious assent from Catholics. It is almost as if the aim were to discover how little one need believe. But surely, as Vatican II urges, it should be the mark of Catholics that they take on the mind and heart of the Church and show gratitude for God’s great gift of the Magisterium.

The calibration of Church teachings that is suggested by distinguishing between the ordinary and extraordinary Magisterium is an important one, but it does not justify any distinction between magisterial, papal teachings that need to be accepted by Catholics and those that do not.
Indeed, to advise Catholics to ignore clear magisterial teachings is to advise them to reject the clear teaching of Vatican II. How ironic that the council should be invoked as warrant for dissenting from the Magisterium when it is precisely the council that rules this out.
To accept Vatican II is to accept what the council says about the Magisterium and the Catholic’s obligation to obey it.

As we will soon see, public and sustained rejection of the Magisterium and of this clear teaching of Vatican II – largely by dissenting theologians – has caused and sustained the crisis in the Church. –from What Went Wrong with Vatican II