On the Catholic side, that's not the case. Communion is open to Orthodox Christians...
Are you serious? I know they acknowledge the "validity" of Orthodox sacraments, but even that acceptance is recent and not accepted among traditionalist Catholics.
Actually, the validity (if not the efficacy) of Orthodox sacraments has been recognized by Rome for centuries. Remember, we have always followed Augustine on this, not Cyprian.
BTW, I don't quite understand the common EO criticism of "validity." It's a simple word meaning "objectively real." In other words, a valid baptism is a real, honest-to-goodness baptism. A valid Eucharist means that the host and the contents of the chalice are truly and actually the Body and Blood of Jesus Christ.
In other words, God isn't running around switching sacramental "taps" on and off. After all, He has those innocent souls living under disobedient shepherds to think about. Should a simple and devout peasant family in Provence suddenly lose access to true sacraments (including baptism for their children!) in 1054 because of a dispute between hierarchs in Rome and Constantinople?
The Catholic position is that the taps will flow if operated by a truly ordained minister with the right form and intention. However, such sacraments are "illicit" (done in disobedience; contrary to church law) if performed by a minister not in full communion with his bishop. God will sort out blame for this, but the taps will continue to flow.
Now, a sacrament may be objectively real, but its efficacy
varies according to disposition. Think of the soul as a sponge, soaking up graces. A holy soul is a soft and supple sponge, ever soaking up grace and expanding. An impure soul is caked with filth, hardened and worn, incapable of soaking up much. So a sacrament may be real, but how much benefit a soul receives from a sacrament varies.
So it goes without saying that those in unrepentant mortal sin, including culpable schismatics and heretics, can receive true sacraments, but they do not receive any grace from them. As for Orthodox Christians, it goes without saying that the Catholic Church sees them in schism---however, today's EO are not (en masse) culpable for the schism that began long before they were born. Thus it is possible for an EO (in a state of grace) to derive benefit from the true sacraments he receives.