To say that everyone outside of visible communion with the Eastern Orthodox Church has no part in Christianity or salvation is just absurd.
We ought to be wary of condemning those (e.g. Roman Catholics) who Patriarch Bartholomew himself has called "beloved brothers in Christ."
Or, if you prefer, we can follow Met. Kallistos Ware in saying “We know who is in the Church but we cannot be sure who will not be," being quick to "affirm that heterodox believers have a deep and genuine faith in Christ and that God will have mercy upon them."
Or we can follow St Augustine in recognizing that "Many sheep are without, and wolves are within."
Or St Theophan the Recluse: "You ask, will the heterodox be saved... Why do you worry about them? They have a Saviour Who desires the salvation of every human being. He will take care of them. You and I should not be burdened with such a concern. Study yourself and your own sins... I will tell you one thing, however: should you, being Orthodox and possessing the Truth in its fullness, betray Orthodoxy, and enter a different faith, you will lose your soul forever."
Or we can follow the OCA's official website's answer (written by my priest): "It is the common teaching of the Orthodox Christian tradition that the Church has no monopoly on grace and truth and love. The Church teaches on the contrary that God is the Sovereign Lord who saves those whom He wills. The Church believes as well that salvation depends upon the actual life of the person, and God alone is capable of judging since He alone knows the secrets of each mind and heart. Only God is capable of judging how well a man lives according to the measure of grace, faith, understanding, and strength given to him."
When the early Fathers (e.g. St Cyprian) taught that there was "no salvation outside the Church," they simply were speaking in a different context than we are. What being "outside the Church" in the 3rd century meant was worlds away from the sorts of denominational splits we're faced with.