The Roman Church may allow Roman Catholics to receive the sacraments at Eastern Orthodox Churches, but the Easter Orthodox do not allow it, do they?
As a general rule Communion is given only to baptized, Chrismated Orthodox Christians who have prepared by fasting, prayer, and confession. The priest administers the Eucharist with a spoon directly into the communicants mouth from the chalice.
Also Orthodox Christianity does not permit its faithful to receive Holy Communion in non-Orthodox communities, whether they be Roman Catholic, Protestant, or whatever. While Roman Catholicism may extend Eucharistic hospitality to Orthodox Christians,
it does not mean that Orthodox Christians are permitted to accept such hospitality.
For Orthodox Christians, the Eucharist is a visible sign of unity;
to receive the Eucharist in a community to which one does not belong is improper.** If one does not accept all that the Church believes and teaches and worships, one cannot make a visible sign of unity with it.** . While many non-Orthodox see this as a sign that the Orthodox Church excludes non-Orthodox from the Eucharist, the Orthodox believe the opposite is true.
Because a non-Orthodox individual has chosen not to embrace all that Orthodox Christianity holds, the non-Orthodox individual makes it impossible for an Orthodox priest to offer him or her communion. It is not so much a matter of Orthodoxy excluding non-Orthodox as it is the non-Orthodox making it impossible for the Orthodox to offer the Eucharist.
They take the whole matter a lot more seriously than we do.