The Eucharist is an expression of communion in the same faith. It is not a means towards a union, but an expression of such a union. Those who are one in faith commune in faith as one in Christ.
The Eucharist would be denied in the Catholic Church to me and to you, not because we are "less worthy" then our Latin brothers, but because neither you nor I profess the same faith as they do.
For the same reason, you and they would be denied Eucharist in an Orthodox church.
Some Orthodox churches will allow Ethiopian or Coptic Orthodox to receive communion of there are no Ethiopian or Coptic churches around, but technically they are not in communion with the rest of the Orthodox world.
In most Orthodox churches, the priest will remind the congregation before offering the Eucharist that only Orthodox Christians, who have properly prepared, through confession, prayer and fasting, can receive the Mysterium.
Your comment above "but a lying, cheating, murdering, raping, unrepentant Roman Catholic is perfectly welcome to and it is proper for him to receive it?" is false only for one reason, unrepenting. For grieveous offenses, such as rape and murder, an Orthodox priest may impose a period of non-communion, not as punishment, but as a time to reflect on their sin and unceasing prayers. It's not enough to simply say "I am sorry."
Confession is not a get-out-of-jail card one can just whip out and go about his business. I hope you realize that, in dealing with the public, it is impossible to set inflexible rules and that each person is a unique specimen and must be seen in context of his or her realities, both spiritual and physical.
I think you are taking this issue of being denied communion way too personally.
Apropos of inter-communing, I think its important to add that in Orthodoxy, living a lifestyle condemned condemned by The Church will also result in a refusal of communion. For example, a couple living together without being married, marriage outside The Church, leading a life of criminal activity, that sort of thing will all result in a denial of the sacrament.
Thanks for your post, Kosta. I think my post sounded like it was charged with more emotion than it really was, so that's my fault. And, I'm sure you saw my post yesterday where I said I had misunderstood what MD was saying.