Interestingly, the EO do not accept as doctrine many things that the Roman rite puts forth and uses *sacred tradition* so support, like the immaculate conception.
Yet they are considered in full communion with Rome.
Somehow.
When Prots are condemned as heretics and Mary haters for not agreeing.
Please allow me to provide some needed background.
First, the obvious: everything that's in big-T tradition is the common patrimony of both the Orthodox and the Catholics, since the Orthodox WERE Catholics --- and the Catholics WERE Orthodox (that is a paradoxical way of saying, we were all in communion with each other) --- for a millennium.
(Note: You seem to have the Byzantines mixed with the Orthodox. Byzantines are now Catholics, Orthodox are not. In any case, the whole lot of us were together for 1000 years.)
The constitutive elements of Big-T Tradition are the same in Greek and Latin, East and West.
The main elements of Apostolic Tradition are these:
That constitutes a preliminary outline of what comprises capital-T Tradition.
Keep in mind that the early creeds and synods, and the Nicene Council, historically *preceded* the canon of Scripture.
Read that again: the creeds preceded the canon of Scripture.
Do you understand what that means? It means the canon was formed based on what the Church already believed in her creeds: these creeds provided the criteria which tested and verified the authenticity of various purported Scriptures (and not vice-versa).
Therefore to accept Scripture is to accept Tradition.
Hit the delete button on Tradition, and Scripture disappears from your screen.
The creeds are a good way to "see" the content. Orthodoxy and Catholicism have the Creeds (Apostles Creed, Nicene-Constantinopolitan Creed, Athanasian Creed) in common, as well as the first seven Ecumenical Councils and all the Fathers of the Church from the first millennium of Christianity.
As for Immaculate Conception: consider Mary as Immaculata and as Panagia. Different languages, similar devotion. I see here convergence, not basic disagreement.