And so despite the fact that there are claims, on all sides, to the contrary, the Church has decided that rather than keep the anger going, we shall release our centuries of bad feelings and embrace Orthodoxy as true Sister Churches...not with the fullness of union...but with sufficient fullness to warrant communion.
Thank you for your answer. But this raises another question. That seems to imply that there is some kind of hierarchy of doctrines in Catholic dogma and that one can somewhat dismiss not-so-important doctrines without losing salvation or communion with Rome. If so, doesn't that render papacy to one of those not-so-important doctrines since we don't accept it?
Not ever word or act of the Catholic Church is immutable. Not every word of every ecumenical council is absolutely written in stone. Not every canon carries doctrinal weight. Some are some are not.
The ordination of married men is mutable.
The ordination of women is not.
Papal infallibility and primacy are part of de fide doctrine, which means that we are bound by the truth to accept this doctrine as it has been defined over time, and more than that: we are asked to accept it in faith as it works to support the core doctrine of the Church which are the Christological doctrine.
The hierarchy of truths does not determine some sort of rank order of what may or may not be believed.
Rather the hierarchy of truths helps to show us the wholeness of our doctrinal teachings and how and where they fit in relationship to the core Christological doctrines, and how they support those doctrines.
These are the formal teachings.
To accept a teaching with assent of the will and intellect means that we take a teaching as it is given to us and try to see how it might be true, how it might fit well with other teachings, and how it might well serve the lives of the faithful. We are asked to first think about a thing in a positive light rather than being self-willed and working hard to see how it might be wrong. It does not mean that we cannot discuss these things and even disagree with certain aspects of the teaching, and to do so quite actively unless we have been asked specifically not to do so.
To accept a teaching with the assent of faith or de fide, is essentially asking the faithful to go through the same process as the assent of will or intellect, but to lock it in even more clearly and not ever to call that teaching by the name of heresy, even if we do not fully understand or agree with it. We may think about it, talk about it, but never work to divide the Church over it.
I hope this is helping a little.