People have already commented on the issue of unity. On top of this, there is another more important layer.
It is true that the Eucharist is essential, but receiving it is no light matter. Consider this passage from 1 Corinthians:
The Church asks non-catholics
and also Catholics who are not in a state of grace not to receive communion for the safety of their immortal souls, and has done so from the beginning as the passage above illustrates. Non-Catholic Christians (with the exception of the Orthodox Christians) have not been taught to understand what the Eucharist is. How can someone “discern the body” if she does not know what the Eucharist is?
It is also extremely unlikely that a Non-Catholic/Orthodox Christian would have been to confession to be absolved of any mortal sins that would impede him or her from receiving the Eucharist worthily. This is very serious, because
a person who receives the Eucharist in a state of mortal sin or without belief receives no grace from the sacrament. In addition, by receiving unworthily, he commits the sin of sacrilege (source:
ewtn.com/faith/teachings/euchb2a.htm)
Asking people to refrain from the Eucharist is not a reflection of an exclusionary attitude, but rather an appropriate result of the Church’s priorities and love and concern for people. It’s really quite logical. We don’t invite people we care about to do things that might harm them. Where we go in the next world is the top consideration here. Temporary feelings of inclusion are not worth risking someone’s eternity.
Those who desire the Eucharist but cannot receive it, either because of personal sin or because they are not in full unity with the Church should consider that desire to be a gentle invitation from God to break down whatever barriers prevent them, such as receiving the Sacrament of Reconciliation or by entering into full communion with the Church.