Do the Eastern Orthodox go to heaven?
It’s possible, although they wouldn’t be saved on account of their distinctive Eastern Orthodox Christian beliefs. All salvation comes by Jesus Christ and through his one Catholic Church. The Catechism of the Catholic Church elaborates on the possibility of eternal salvation for non-Catholic Christians and non-Christians:
How are we to understand this affirmation, often repeated by the Church Fathers? Reformulated positively, it means that all salvation comes from Christ the head through the Church which is his body:
Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and baptism, and thereby affirmed at the same time the necessity of the Church which men enter through baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.
This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church:
Those who, through no fault of their own, do not know the gospel of Christ or his Church but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience—those too may achieve eternal salvation.
"Although in ways known to himself God can lead those who, through no fault of their own, are ignorant of the gospel, to that faith without which it is impossible to please him, the Church still has the obligation and also the sacred right to evangelize all men" (CCC 846-48, emphases added; footnotes omitted).