Read and compare Orthodox and Catholic Catechisms. If they are not the same, our teaching is not the same. Unless both the East and the West teach the same faith, they cannot be in spiritual and theological communion.
The Filioque would, of course, have to be removed because it is at the very heart of our understanding and teaching of the Trinity, that is, the Monarchy and the Divine Economy -- that the Father, who is the Supreme Wisdom (Sophia) is the only Source and Cause of everything, that the Wisdom eternally begets the Word and that the Spirit of God eternally proceeds from the Wisdom. That is the core and everything else is ex post facto.
Then there is Immaculate Conception. We both believe Mary is Immaculate and Ever-Virgin Mother of God, but that's where our "communion" stops, without going into the details that have been rehashed over and over.
Then there is the purgatory where souls are being flamed to the satisfaction of God (how preposterous!). Needless to say, the Church somehow didn't "know" this in earlier centuries. Makes you wonder what else the Church doesn't know!
Then there is the dogma, yes dogma of papacy. Dogma means that every member of the Church has to believe in it. How can we be in "communion" if the "other lung" doesn't believe it, and doesn't teach it?!
Our Sacraments may be the same, but our teaching of them is not. Take, for instance, the Eucharist (does it get any more basic than that, aside from the Filioque?): we both believe in the Real Presence, but that's where our "communion" stops. The doctrine of transubstantiation is alien to the Church of the Seven Councils. It is a philosophical exercise in futility to "explain" a Sacrament (Divine Mystery). Believe me, humans are not that smart!
We believe that we know all God wanted us to know about Him and that His Word delivered the faith to us through His Apostles. That faith is contained in the Holy Tradition of the Church (and by the Church we mean ekklesia, the clergy and the laity), the written and unwritten knowledge, the Sacaraments, and the explanations (not additions) of the Councils. We therefore do not believe in the "depository of faith" from which new "knowledge" or "better" faith can be derived.
We don't think the same and we don't teach the same. Someone who looks at our outwardly differences may conclude that we are two expressions of the same faith. We are not. A more careful look at the essence of our teachings makes that very clear.
So, in a nutshell, to answer your question: the West would (again) have to embrace orthodoxy in doctrine and praxis, as Kolkotronis correctly observes, for us to be one again. We are still the Church of the Seven Councils. In our eyes, you left the other four Patriarchs and then added unorthodox teachings. In your eyes, we remain frozen in time and are "missing" all the beautiful things that were added to the faith since the 11th century.
You acknowledge us as true, but "schismatic" because the Church that was true in the 8th century it is still true, but disobedient and "deficient.". We acklowegde you as having true roots, but in our eyes you are the first Protestants! You changed the faith into something that is unrecognizable to us and, therefore, unrecognizable to the Church when we were one and the same faith (before the Schism).
For us to be in spiritual and theological communion with each other, we must profess and believe the same faith; our teachings must be the same. It is not possible to be in communion if one side of the Church believes in purgatory and the other doesn't. Talk about a schizophrenic church!
One of us is (more) deficient than the other. We can't both be equally wrong. Only time will tell and perhaps we shall never know -- at least while on earth, and then it may not matter (no pun intended).
An excellent exposition, as usual, Kosta.
I wonder what God thinks of all of this.
Our squabbling over dogmas and rites doesn't amount to a hill of beans if God feels more vexed by it than glorified.