On the IC the Orthodox will not accept the RC dogmatic definition because it dogmatizes an Augustinian view of Original Sin thru the back door, which isn't consistent with our Orthodox Byzantine theological tradition.
Why is this? Dogmas are, properly speaking, about God. The only reason for a "dogmatic definition" about the Theotokos would be if it were to have an impact on what we believe about God Himself. Well, this is what the I.C. dogma is ... it is essentially a dogma designed to preserve the absolute sinlessness of Christ's human nature from the time that it was en-hypostasized into the Hypostasis of the Logos. Because the Augustinian tradition, and the notion that Original Sin was a "stain" or a "macula" on the soul, it was offensive to orthodox Christology. Therefore it was important, almost critical really, for RC theology for the humanity of which Christ partook in becoming incarnate -- namely the humanity of the Theotokos -- be preserved free from this macula, or stain, so that Christ's humanity itself was preserved free as well. Therefore from the perspective of an Augustinian theological perspective on Original Sin, the I.C. makes sense, and perhaps is even necessary.
Byzantine theology differs from Augustinian most prominently in its casting of Original Sin. Byzantine theology does not see this as a "stain" in the way that Augustinian theology does, and does view any human nature as "stained" in the way that Augustinian theology did, or may have been understood to have done. Therefore we do not see that any dogmatic definition concerning the status of the Theotokos in this matter is necessary. We can agree with Roman Catholics that the Theotokos was preserved from any "stain" of Original Sin, but we disagree that she was unique in this way. We can agree also with Roman Catholics that the Theotokos was free from actual sin during her lifetime, and that this was because she was given this gift as a singular act of divine grace. But we do not believe that this made her humanity different, in the sense that it was not subject to Original Sin like that of everyone else. From our theological perspective, this sets everything on its ear ... the Theotokos becomes an ueber-human, really essentially different from everyone else because she is not subject to Original Sin, she is not a member of "fallen humanity" at all. This is why Orthodox say that the I.C. makes the Theotokos the great exception from, and not the great exemplar of, the human race as we know it on this Earth.
This creates serious problems for Orthodox soteriology as well, because our theological perspective is that salvation is achieved in and through theosis, whereby the believer is Christified, or rather his/her humanity is molded to that of Christ through communion with the Holy Trinity and by means of the divine grace that this communion bestows over time. The model for this idea of salvation is Christ himself -- namely, by taking fallen humanity in the form of a fallen human nature into himself and uniting it with his infinite, pure, holy, immortal divine nature, he Christified it, deified it, redeemed it, and saved it. But if He didn't unite with our fallen nature, how was our fallen nature saved at all??? Much of the Christological debates of the first millenium were concerned with ensuring that our theological terminology about Christ preserved the reality that he was fully human and fully divine ... because without this the whole idea of salvation is placed in jeopardy: if Christ were less than fully human, humanity was not saved by union with Christ, and if Christ were less than fully divine, again humanity is not saved because there was no union with God in Christ. From the perspective of Byzantine theology, the I.C. interferes with our understanding of soteriology because it infers that Christ did not assume our fallen human nature into himself, but our unfallen nature, which leaves the status of our fallen nature ... unredeemed.
You see, we see that all redemption comes through communion with Christ ... the same for you and me as it was for Christ's human nature. The difference is that the salvific act in Christ's person Himself began at the time that his human nature became en-hypostazized into the Hypostasis of the Logos and through that (and continued throughout his life, death and resurrection, which Orthodox see as essentially one, drawn-out, salvific act), whereas with us, because we are not taken into Christ's Person, or his Hyspostasis, but rather remain our own persons, we are saved through the divine energy/grace given through communion with the Holy Trinity. But the idea of salvation is the same in each case -- namely union of our fallen humanity with Christ. If Christ somehow did not assume our fallen nature and deify it by bringing it into his pre-eternal Hypostasis and therefore into communion with His divine nature, living and dying with it and resurrecting it to eternal life, then our notion of our own salvation as the deification of our own fallen humanity to make it conform to Christ's humanity is placed at risk, because it is, in any case, a replication of the model of what happened when Christ became incarnate, differing only in the means (i.e., grace through communion for us as compared with deification through en-Hyspostasization in the Person of Christ/Logos).
So where does that leave us? Well, at a minimum it means that we cannot accept that the I.C., as defined by Rome, is a *universal* teaching. It clashes too much with Byzantine soteriology and our theology of Original Sin. We *may* be able to accept that it is an acceptable articulation of Latin theology, on the basis that the Augustinian model, while never really utilized much in Byzantine theology, nevertheless was known during the period when the Church was unified and was not condemned, but accepted, it would seem, as a non-Byzantine theological expression. But that would mean that it is a *latin* doctrine only, not a universal dogma.