Instead of replying with my own words to your query, I reply with the words of the Catechism, Part 1, Section 2, Chapter 3, Article 9, Para 3, Sub 3, Heading 5, 846-848:
Outside the Church there is no salvation[Source]How are we to understand this affirmation, often repeated by the Church Fathers? Re-formulated 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."
Q. I'll take it, then, that you don't take John 6:53-56 literally, then
A. 1. Understood literally, John 6:53-56 says that those who have not physically received the Eucharist have no chance of living in the Kingdom of Heaven.
2. But we know from other passages of Scripture that Heaven is inhabited (among others) by Moses, Elijah, John the Baptist, St. Dismas, Enoch, and others who died prior to the institution of the Sacrament.
3. Therefore, a literal understanding of John 6:53-56 is not 100% correct.
My own personal belief (and keep in mind that I am the layest of laymen) is that those who believe that Jesus is God and who know that the Eucharist gives life and who yet refuse it are guilty of refusing salvation.
As for those of other religions: we know that Jesus burst the gates of Hell and proclaimed the Gospel to the dead. Since all men die, it therefore follows that all men will at some point hear the Gospel and be presented with the Reality of Jesus' Passion and Resurrection for the atonement of sin. At that point, they will choose either to accept Him or reject Him. It may be that as we die, in our last, fleeting moments of consciousness, Christ appears to us and makes plain His love for us, offering Himself as our saving Sacrifice. At that instant, if we partake of His Flesh and Blood, we will live.
We don't know how Christ offers his Flesh and Blood to those who did not have the chance to commune with Him due to distance in space and time; we only know that He does offer it to all men oof all times. Being God, He is perfect; being perfect, He is perfectly just. Being perfectly just, it seems logical to assume that God is not going to bar from Heaven those who through no fault of their own (ignorance, other religious training, sincere agnosticism, etc.) have failed to see Who Jesus is and What He offers us.
We can't know who is going to Heaven. We can know that every one of us who makes it to Heaven will make it there by following the lead of Our Lady, who, when presented by God with the choice of accepting Jesus or rejecting Him, replied "Let it be done unto me according to Your will".