I think it should go without saying that those who are not members of the local Church, or members of other local Churches in communion with them (if they are travelers) should not be communed. This is a principle that has theological/ecclessiological underpinnings, and it is abundantly reflected in the canonical tradition of the Church.
Saying this, there is a danger in letting every perceived misdeed of a Priest be grounds for scandal. While it is eminantly up to the Priest himself to avoid causing scandal, if he fails in this, we should try to rise above it and not pour oil on the flames. Spartacus has a point, in so far as there could be things about the situation brought up at the begining of this post which are not apparent, and butting one's nose into it without invitation is not called for. There is going to be much, both good and bad, which was not apparent to us in this life.
At the same time, the phenomenon of communing non-Chalcedonians has become something of a pandemic in some parts of the Orthodox world. I wouldn't say this is due (mostly) to an overtly syncretistic ideology on the part of those Priests doing this (or the Bishops who let it happen), but due to profound misunderstanding on the part of those allowing this. There are some Orthodox academics and Bishops (and unfortunately clergy in the parishes influenced by the banter eminating from these) who really believe that the "non-Chalcedonian" situation has been setteled, and that all that is left are formalities still being sorted out. In other words, the Priests who allow this (typically OCA and Antiochians, but this is not at all unknown in the GOA as well), often genuinely believe that the non-Chalcedonians are "Orthodox Christians" without any qualification. This is carelessness on their part, and they are playing with fire - they are certainly violating the rules of the Church in proceeding in this way.
Unfortunately the problem is being irritated on a much larger scale by the activities of the Patriarch of Antioch himself. The various agreements signed between his representatives and the non-Chalcedonians basically amount to saying formally what the errant Priests who commune non-Chalcedonians tacitly believe - that this is all an issue of semantics (and more to the point, always has been which I think is the truly false conclusion), and as such "we" (in this case the Patriarchate of Antioch) can proceed as it see's fit.
I can sympathize to some extent with this thinking, since in terms of praxis the non-Chalcedonians are not a problem (as far as I'm aware). Also, my experience is that the non-Chalcedonians I have spoken to, in many words materially do believe in the faith of Chalcedon. What I think is manifestly not true, is that this always has been and universally was the case even going back to the events which caused the non-Chalcedonians to be seperated from the Orthodox Church, and that it is not necessary for these "materially" Orthodox believing modern non-Chalcedonians to be in unity with the Church while remaining precisely this - non-Chalcedonians! The Holy and Ecumenical Councils rightly divide the faith - thus, even granting to our modern non-Chalcednian friends that they materially (even if talking in circles and using different terminology) agree with the Church, there can be no visible formal unity with them, if they do not visibly, formally profess the same faith. Even the most liberal, "economia" receptions of seperated communities into the Church (such as is evidenced in long standing Russian practice) involve at least one thing - repudiation of falsehood and a clear, unambiguous confession of the Orthodox faith, whole and entire, including an affirmation of the Ecumenical Councils and the traditions of the Church.
To simply say that such an affirmation in so many words is not necessary, is to put to a lie the idea that any real "visible unity" exists! What "unity"?! Such a union is bogus - what you have maybe is "agreement" (even in large part), but not the visible, canonical unity of the Church which is what any unia should be working to effect.
Orthodoxy is not Papism - She does not appeal to "communion with this or that Patriarchate(s)" as the litmus test of authenticity. Fundamentally it is a fidelity to truth, and the confession of it, which effects and manifests this unity. Thus, from an Orthodox p.o.v. simply "concelebrating" and effecting an administrative unity is meaningless. Not only does this not effect unity, but it actually drags those Orthodox who involve themselves in it out of the Church, by creating schism. And I fear this is precisely what is going to happen if the Antiochians do not put a stop to this and reconsider - the Patriarch of Jerusalem has already written strongly worded letters to the Patriarch of Antioch, adominishing him to stop this. We need this kind of mischief (that the Antiochians are up to) like we need a hole in the head. Such ill advised pandering to heterodoxy has already caused divisions in the Church, and very painful enduring ones at that.