We cannot be in communion unless we share the same faith. With all the dogmas and theological customs introduced by those dogmas we no longer recognize an Orthodox Church when we walk into your Church.
But how tightly would you define the "same faith"? Does it mean that we must be in complete agreement in matter of theological speculation? I have seen the comments elsewhere, I do not remember if they were yours or by someone else, that "we do not do theology the same." But why should this be necessary as long as we agree on the essentials of the faith? I do not know the situation among the Orthodox, but among Catholics there are different schools of theology. We Catholics do not all do theology the same. We still agree, however, that we share the same faith.
There was a lot more "tolerance" between the east and the West in those days.
But why can we not return to that tolerance today? The Orthodox constantly complain about the introduction of perceived novelties by Catholics. From a Catholic perspective, however, the introduction of the intolerance on the part of the Greeks toward the Latins in 1054 was a novelty. The issues with which we have been debating over the past one thousand years were known for centuries before the split. For six hundred years they were not considered grave enough to justify a rupture in Church unity. Why must they be considered so now?
The Church of the latter hale of the first millennium was practically separate because of the language if not by theology, so many of the inovations, and even father were not known.
From about 450 AD almost no one spoke Greek in the West and certainly the same was true in the East for Latin. For example, St. Photius didn't understand Latin. A bad translation of the Greek word "ecumnical" as "universal" instead of "imperial" caused serious strain in the West when the Bishop of Constantinople (Ecumenical Capital, meaning Imperial Capital) was given a title of "Ecumenical Patriarch."
St. Augustine remained virtually unknown in the East until the 15th century simply because no one could read him, etc.
But the Church was united in theology. Your Church added dogmas which we do not accept. Dogma is an obligation -- and the dogmas added especially in the last 200 years or so were more conducive to widening our split than narrowing it. The dogma of Immaculate Conception and papal Infallibility is what I am talking about, in addition to the insertion of Filioque centuries prior.
Until such dogmatic teachings are reconciled, we are not the same faith, because you must believe that which we don't.