As has been pointed out, Christians who have the same belief as us (Eastern Orthodox) and present themselves *of their own free will * (that's very important, so we cant be accused of trying to 'poach' worshippers) are entitled to receive communion from the Catholic Church.
No-one else should receive it under any circumstances.
If someone who doesn't believe in the real presence takes communion, they disrespect God by denying His presence and they show themselves to have no integrity, through insisting on taking part in something which they don't believe in. Also, their actions are not respectful of the belief of others present.
If someone who does believe, but is not a Catholic, takes communion, then they are essentially profaning the sacrament, via partaking of it whilst not in an appropriate state of grace. (I think this case is similar in some ways to a Catholic in a state of motal sin taking communion). To be fair, this situation can often occur through ignorance, by the person not knowing or understanding the "rules".
When I first started going back to Church, (years ago now), I soon realised that I had been taking communion when I really should not have been (I just started attending mass again, I didn't think to go to confession first or even prioritise this - poor catechesis).
This was because I had not practised my faith for about 13-14 years at that point, and had naturally committed all kinds of unspeakable sins during this period. I should have gone to confession prior to taking communion, as - without a confession - I was taking communion whilst unworthy, which is offensive to God.
Naturally then I had to add error this to my confession. I was worried the Priest might "go mental" (as we say in Scotland) , but it was "like being stoned to death with Popcorn" (to misuse a ++Sheen quote).
Priests who knowingly break these rules probably do not believe in the real presence and so should not really be Priests at all. Whilst well meant, their actions only confuse the faithful and indeed those people/guests whom they are breaking the rule for.
Its good if we all stick to the roolz :D