There is no such distinction. The teachings of Tradition, Scripture, and the Magisterium are NOT divided into negotiable and non-negotiable teachings. This terminology does not come from sound Catholic theology, nor from magisterial teaching. It seems to have arisen from an effort by some Catholics to explain Church teaching, on issues that are controversial in sinful secular society, using common parlance, without any theological terminology. That is a mistake.
No teachings of Tradition, Scripture, Magisterium are “negotiable”. Therefore, we cannot say that some subset of teachings are the “non-negotiable” ones. This term has been applied to Church teachings questioned or rejected by secular society (and by secularized Catholics). But it is a misleading term.
The teachings of Tradition and Scripture are entirely inerrant; there is no possibility of error in all that Sacred Tradition or Sacred Scripture asserts as true. If there is an apparent error, the mistake is not in Divine Revelation, but in the mind of the individual. All the teachings of Tradition and Scripture are material dogma.
As for the teachings of the Magisterium, these are divided into infallible teachings (formal dogma) and non-infallible teachings. The non-infallible teachings are subject to a limited possibility of error, but never to such an extent as to lead the faithful away from the path of salvation. The non-infallible teachings are non-irreformable, meaning that a particular teaching or point within a set of teachings can change, improve, or be revised.
The infallible teachings require the full assent of faith (theological assent) because these teachings are certainly true and are important to a holy life and to the path of salvation. The non-infallible teachings require a different type and lesser degree of assent: religious assent. These non-infallible teachings are reliable; they have only a limited possibility of error.
Why should anyone be required to believe that which is not certainly true? There are several reasons. No error or set of errors in non-infallible teachings can lead us away from the path of salvation. The non-infallible teachings contain important truths; the faithful cannot wait for an infallible declaration from the Magisterium on every question. Moreover, the Pope and the Bishops are sinners in a fallen state. We cannot expect God to intervene at every point in time, concerning every teaching of every Pope and Bishop so as to entirely exclude all error. Such a requirement would also exclude individual Bishops from teaching at all, since the prerogative of infallibility is not given to individual Bishops, other than the Pope. And finally, if a faithful believing and practicing Catholic understands that a non-infallible teaching is in error on some point, based on teachings of higher authority in Tradition, Scripture, Magisterium, then that Catholic is not required to believe that particular point.
However, the ability to faithfully dissent from a non-infallible teaching does not make that teaching “negotiable”. All the teachings of the Church require assent from faithful Catholics. The distinction between infallible and non-infallible teachings is not a distinction between what is and is not negotiable. And infallible teachings are not accurately described as “non-negotiable”, as if it were merely a matter of what one must accept. The infallible teachings are certainly true; they are important truths taught by God through Tradition, Scripture, Magisterium. To call a non-infallible teaching “non-negotiable” seems to put those teachings of truth in the category of rules that one cannot bend or break, versus rules that admit of exception.
Theological terminology has developed in the Church and in magisterial teaching because it is useful in order to express the truths of Divine Revelation accurately. It is a disservice to the faithful to dumb-down terminology to the point of distortion and misrepresentation.