As mentioned, I kept thinking about this question, especially after I read some of the comments on the Facebook thread.
The whole thing seemed to start with an assertion -- in a link that I did not follow -- that there was nothing Biblical about the way the Catholic Church handles Holy Communion; namely, that one must be a member of the Church and in a state of grace to receive the Eucharist. This assertion is not correct and it's based on a fallacy in any case. In one of his letters St. Paul talks about the need to discern before approaching the Eucharist; I am not going to say much about that, because so much has been said before on that passage.
But I will point out the fallacious idea that it somehow proves something if X is or is not referred in Scripture. For one, all that really means is to say, it was mentioned in the Bible in a way that the one making that claim will recognize. So for example, many say that the Immaculate Conception (Mary conceived without original sin) isn't in the Bible; but in fact, it is. But when you start pointing that out, your interlocutor will say something like, oh well, that isn't what that passage really means...which is moving the goal posts! And it reveals the futility of the whole "is it in the Bible" argument, because that soon becomes a question not of whether it's "in" Scripture, but rather of interpreting Scripture, and who settles those questions.
It's not nice to be rude, but sometimes a rude question can be useful: when someone says, "show me in the Bible," the correct (if impolite) question is, "who died and made you boss?" My serious point being that so many of our Protestant brethren operate from assumptions that they aren't used to having anyone challenge, and this is one them: the assumption that everything Christians believe is supposed to be in the Bible (which we can refer to as Sola Scriptura). That assumes our Faith begins with the Bible, when in fact, our Faith begins with God's revelation to people, some of which was written down. The Bible is not the source of our Faith; but it certainly is an essential witness to it.
By the way, it was interesting to see another way this appeal to Scripture broke down in that thread: once someone pointed out what St. Paul said about who can receive Holy Communion, someone came back with, oh that's Paul but what about Jesus? Pitting the Apostles against Jesus -- as if the latter is the only one we can trust -- is in every way incoherent. You and I know next to nothing about Jesus apart from the Apostles. They are how you and I know about him. So if we must distrust them...then we have nothing. And who was it who set it up that way? Jesus. He chose not to write his own memoirs, or for that matter, tell anyone to do so (at least, as far as the Bible tells us!). He simply spent a lot of time with them, and entrusted his entire enterprise to them. Either we trust them or we don't; and if we don't, I don't know what is left of Christianity.
Sola Scriptura is not authentic Christianity and it isn't even biblical. So while there are times I might be willing to respond to a question premised on it, it's fair to point out the falsity of the premise and that's what I'm doing here. Why should what the first Christians did with the Holy Eucharist -- and which Catholic and Orthodox still practice -- be condemned because it doesn't measure up to a doctrine invented in service of the polemics needed to justify breaking the unity of the Church in the 1500s?
It is quite understandable that few Christians of any stripe know this. Nevertheless, a little history is important.
Martin Luther and the others who rose up around the same time were all arguing for something radical: either a complete reworking of the Church, or else the breaking-apart of the Church. And the natural question to ask was, what can justify such radicalism? Luther, of course, could and did point to abuses; but one can legitimately say, fine, but you're going much further. And Luther himself was put on the spot and asked, would he accept the judgment of an ecumenical council to resolve his concerns definitively? And he refused; he said, "unless I be convinced"; he made his own judgment (and by implication, any Christian's) as final as the teaching office of the Church -- and that teaching office Scripture shows clearly was entrusted to the Apostles, led by Peter, and to their successors. In order for Luther (and others) to justify their drastic action, they had to magnify the crisis they purported to solve; suddenly, it wasn't about modest problems or changes, but in fact, the entirety of Christian doctrine and worship was riddled with error and corruption. You don't justify a revolution with only peripheral problems. And so the result of that revolution was a re-invention of Christianity in many ways.
Fast-forward from the 1500s to now, and there are quite a lot of Christians -- sincere and admirably devoted to Jesus -- whose understanding of the Faith is riddled with lots of presuppositions that never get challenged, like sola scriptura and open communion, and it comes as a real shock to them to be told that what they imagine as authentic Christian beliefs are nothing of the sort.
So, I'll just throw down the gauntlet here as follows:
When the Catholic Church says that one must be "in communion" with the Catholic Church, and in a state of grace ("in communion" for our purposes here meaning, you belong to the Catholic Church), in order to partake of the Holy Eucharist, she is simply continuing what was the practice of Christians from virtually the beginning.
How do I know? I point to the history of all the ancient churches, including the Orthodox and other ancient churches, and I point to copious ancient writings, and all the liturgical sources we have; anyone who wants to read this can keep him/herself very busy. The ancient practice was, if anything, even more severe: the "Mystery" of the Eucharist was so precious that non believers were dismissed at a certain point, including those preparing to be baptized, and not allowed even to be present! We have many ancient Easter homilies discussing this, and explaining the mysteries to the neophytes, who are able to observe them only after they are baptized and confirmed.
So one perfectly reasonable response to someone who says, why can't non-Catholics come to Holy Communion is to ask, why do you think the practice of Christians at the beginning and from the beginning should be overthrown? (Rude version: "who died and made you boss?") Of course, they will likely not know, or be ready to believe, that this was the early and continuous practice; but you can do as I have done here and say, "it's all there -- go do some reading." On the sidebar is a link to Catholic Answers, and this is their specialty: curating lots of writings from the early Church on these various subjects. You could go to their website as a start.