"Then why are Catholics and Orthodox not in communion if you have the same core of faith?"
It is because the Orthodox and Catholic conceptions of what constitutes the core differ significantly.
For Catholicism (painting dangerously broadly), the core boils down to a body of dogma and to a assenting relationship with the Pope/Magesterium. So, from a Catholic standpoint, since Orthodox written formulations of basic dogma is pretty much the same, with room for differences in interpretation, the 21st century approach is to call it good and move for intercommunion.
There is the sticking point of the Pope/Magesterium, of course. One must ask the following questions: 1. Is Papal infallibility a dogma of the Church according to Catholicism? (Yes) 2. Do the Orthodox resolutely, consciously, willfully, vigorously, and in full knowledge and awareness reject this dogma, both in letter and spirit? (Yes) 3. What do we call people who willfully, consciously etc. reject a fixed dogma of the Church in spite of many, many attempts at correcting or coaxing them back into the fold of right belief?
Be that as it may, I would move on to say that for Orthodoxy, the core is the totality of living tradition. It is the inner spiritual life of the Church. This is sometimes not appreciated by the average outside observer (I wouldn't include you, stripes -- I realize the rhetorical nature of your question), since our inner spiritual life is inextricably linked with the rich "outward" life of fasting, liturgical prayer, incense, pannikhidas, blessings, confession, communion, prostrations, vigils, prayer ropes, etc...
The Orthodox conception of what constitutes "the core" is very all-encompassing and holistic. It cannot be encompassed by written formulations of dogma and doctrine to which one does or does not give intellectual assent. It isn't that we can't conceive of a Western equivalent to this spiritual core (far from it -- some of the most devoted students of western liturgics and spirituality in their pre-schismatic forms are "Eastern" Orthodox Christians), it is just that most of us don't see an analogous core at this time -- although we do like that new Pope better than anything we've seen in a long time. (What an irony that he is a German -- a "Frank"!)
I wouldn't choose Kosta's image of a "shell," although I certainly think I understand what he is getting at. I would prefer to say that for us it is all "core."
In short, because the Catholic core is smaller than the Orthodox core, at least at this moment in history, they are prepared to accept Orthodoxy as we are. Again, with the exception of the infallible Papacy -- I really don't see an easy way around that one, for either side. It is one thing to say that we Orthodox can keep out long beards, long services, clouds of incense, icons, and filioque-less Creed. It is quite another to say that we can come into communion with Rome while continuing our resolute rejection of Papal infallibility, or even of Papal supremacy/universal jurisdiction.
Agrarian, you have certainly answered Stripes' question much more inclusively than I have, and that is good. It shows that in addition to theology and ecclasiology, it is ultimately the praxis, the life in the Church is ultimately the all-encompassing concept of what is known as the "Orthodox Church," and that, looking at the Big Picture, that Church is very, very different from the (Latin) Catholic Church as we know it.
I am not sure – given the virtual apartheid that existed linguistically and in day-to-day life of the Greek and Latin Churches since the 5th century A.D. – that a Greek would have recognized the same Faith in Rome or Spain even in the first millennium, let alone understand the language of the Liturgy, yet the Churches were in full communion.
You see, communion is not a means of achieving unity but an expression of it. That's why we cannot allow our Catholic brethren to partake of it in Orthodox Churches. Not yet anyway. Being in communion simply means that, regardless of the praxis, our bishops hold that those bishops with whom they are in communion teach the same Faith and confomr to the same canon.
However, there were periods, lasting even decades, in the history of the Church in the first millennium when the East and the West were not in communion for reasons that were not theological, as is the case with the current issue of the so-called Macedonian and Montenegrin "churches." Oh, for sure, theologically, they are Orthodox, but they have claimed autocephaly in a way that is not prescribed by the canon.
If a bishop finds another bishop to teach that which he believes is wrong, the bishop will ex-communicate the other bishop until such issue is resolved.
The term excommunication has acquired loaded meanings as you noted in one of your earlier posts, but it only means that one bishop believes the other either teaches or does something that is theologically or ecclesiastically wrong.
But that does not excommunicate the bishops from the entire Church. I am sure that St. Augustine and St. John Cassian were not in communion. Yet, both are saints in the Orthodox and Roman Catholic Churches. Moreover, John Cassian was condemned for his semipelagianism by the Local (Latin) Council of Orange, as was most of the teaching of St. Augustine by the Orthodox Church in the 15th c. and neither were "stripped" of their sainthood by either Church.
It is only when the entire Church Community backs one bishops that the other bishop can be considered outside the Church, which is the case between the East and the West at this point, although the event of 1054, as I mentioned earlier did neither imply, nor aim at such exclusion because the excommunicatios issued were (1) legally invalid and (2) directed at specific bishops and not the entire Greek or Latin community.
In the period of the undivided Church, such disagreements were addressed by Ecumenical Councils and resolved. Obviously such a council was convened even in the informally divided Church, in Florence, but failed on the local level (the Orthodox laity and lower clergy rejected it).
The real Great Schism that widened the gap between the two Churches occurred not in 1054 but in 1870 (Vatican I), when the ex-cathedra infallibility of the Bishop of Rome was added (and eventually dogmatized) to the original topics dealing with liberalism, relativism, modernism and lack of piety for the Eucharist.
If we profess the same faith, outward differences in our approach to praxis should not be a justification to exclude a member of the other community Eucharistically. Outward expressions of our faith, the praxis, the manner of worship, etc. cannot be insisted on as long as they do not violate the Holy Tradition, i.e. do not clash with Apostolic teachings, the Scripture and the pronouncements of the Ecumenical Councils.