Quite frankly my brother you can’t even tell who is part of the body even in the members of your church.
While someone could lie, we can take reasonable precautions; we can’t don’t what their spiritual health is, but at least we know we’re admitting to the Eucharist someone who ostensibly believes, or was taught to believe, and is supposed to believe, and has been taught not to receive if they cease to believe, in the Incarnation, the Trinity and the Real Presence (since we believe partaking of our Eucharist not discerning the Body and Blood would be extremely dangerous). Likewise members of the LCMS know that a member of the Missouri Synod believes or should believe in the Nicene Creed and the Real Presence. And in both cases, that Orthodox, Catholic and Lutheran members believe in other doctrines that we believe are important, most of which the three churches agree on, disagreeing on only a few, for example, the role of the Bishop of Rome or the issue of monergism (but enough to where we are not yet in full communion with each other; this will take time).
Additionally in the Orthodox Church, many churches take the added precaution of requiring members to attend the sacrament of reconciliation, also known as auricular confession, before the Eucharist. Likewise, Orthodox, Lutherans and Anglicans include a congregational confiteor, where the whole congression prays for forgiveness of their sins (separately from auricular confession).
Auricular confession in the Orthodox Church is something I love, because our clergy are not required to issue penances, and through that sacrament I have been assisted with a great many thing. For example, I no longer have what used to be a horrible fear and revulsion towards hearses. I now regard hearses as, for the most part, beautiful vehicles that we use to transport our loved ones to the place where their bodies will repose until it is time for the Resurrection. I only have a dislike of hearses that are tacky or grotesque in their appearance (recently I saw a hearse being exhibited at a funeral trade show that was disturbing; whoever designed it was sick, I think, but that is another matter). Many other assistances have been provided to me through this means of grace. So requiring it before partaking of the Eucharist is a good idea, and indeed the churches that do require it ensure there is time for this even for people unable to attend the Vigils the night before (which is the usual time), by offering the liturgy during the reading of Terce and Sext.
What all of this amounts to is that we take reasonable precautions. From the parable of the talents, it is clear Christ desires us to be responsible and will hold us to account, and while we confess to being unprofitable servants, we try; we make a best-faith effort to ensure that everyone receiving the Eucharist is a part of the Body of Christ in a proper disposition to receive the Sacrament.
All churches have those that profess to be but are not in the heart
In the Orthodox Church, unlike in some other denominations, no one is ever pressured into receiving the Eucharist (in some Roman Catholic parishes and some Anglican parishes, among others, people who sit out the Eucharist experience peer pressure not to, even if they have a good reason to not partake, but one will never experience this in the Orthodox Church.
I particularly like how the Syriac Orthodox arrange this at some parishes and cathedrals - they often distribute the Eucharist at the very end of the liturgy, after the dismissal, while the hymn Haw Nurone is sung, from the right or liturgical south side of the altar, while who have partaken or are not partaking will exit to the left or liturgical North side of the altar, collecting antidoron (the blessed bread, which is not the consecrated Body of Christ as I explained earlier but rather was historically given as a blessing to help attendees get home, and is a sacramental, like holy water, but not the sacrament itself) on the way out.
We don’t believe in casual communion.
Thus if someone doesn’t believe, and presents themselves for the Eucharist, its on them, since we have taken all reasonable precautions to ensure that those who have received the Eucharist are among us.
Additionally I would add if a non-Orthodox tried to partake of the Eucharist they would probably not be able to do so as their identity would easily be discernable. And they would not likely even be rebuked but assisted; the assumption would be they had approached in error and were confused, and they would be graciously shown to the antidoron. I’m not going to explain exactly why this is because I don’t want to empower people to approach our Eucharist without authorization, but suffice it to say, we are careful (and additionally some of our priests can discern someone approaching with ill intent). Unlike the Roman Catholics, all Orthodox priests are authorized to repulse someone from the sacrament, so instances of our Eucharist being stolen, for example, by those who engage in the occult, are I would say unheard of, for I am not aware of any instance where it has happened.
That said I have no personal objection to the Assyrian Church of the East’s approach, which is to allow anyone who believes in the real presence and the Nicene Creed to partake. There is frequent intercommunion between the Assyrian Church of the East and the Chaldaen Catholics due to the situation on the ground in Iraq where nearly all Chaldeans live and also the majority of Assyrians (Chaldeans are one of the largest of the seven Assyrian tribes historically associated with the Church of the East, which unlike the others wound up mainly speaking Arabic instead of Aramaic, and the Roman Catholics persuaded most Chaldeans to join the Chaldean Catholic Church, which was an archdiocese of the Church of the East which broke away from the rest and entered into communion with Rome). Thus there are areas which are predominantly Syriac Orthodox, areas which are predominantly Church of the East, and areas that are predominantly Chaldean Catholic.
Likewise, in Turkey, the Syriac Orthodox will give the Eucharist to Roman Catholics at their parish in Constantinople, because the nearest Catholic church is some distance away, and Catholics will always give the Eucharist to any Orthodox or Assyrian Christian disposed to receive it, and other sacraments as well.
So essentially where we are now is in the process of establishing trust with the Roman Catholics to where we can reciprocate their offer of what they call Eucharistic hospitality, just as we presently do in the case of relations between the Antiochians and Syriac Orthodox and the Copts and Alexandrian Greek Orthodox.