Canon lawyer Ed Peters writes at First Things about the appropriateness of denying Communion to Catholics engaged in public behavior that would seem to exclude them. Mr. Peters points out that this issue has been around for quite a long time, and was first raised in the case of Catholics who have been divorced and are now living in civil marriages.
This problem of irregular public relationships has certainly not gone away, but now in the spotlight is the case of Catholic politicians who ardently support abortion, euthanasia, the redefinition of marriage to include unions that cannot possibly be marital in the sense that Catholics understand them, and other evils that (unlike harm-causing acts such as warfare and executions) cannot be reconciled with any interpretation of Catholic moral doctrine.
Many Catholics who support untraditional marriages, Pelosi’s near-perfect pro-abortion politics, or Rainbow Sash-style activism profess outrage at seeing the Eucharist “used as a weapon” against fellow Catholics. Others, however, are appalled at seeing such markedly contrarian Catholics take Holy Communion.
Mr. Peters states that he, along with Raymond Cardinal Burke, holds the view that sometimes a minister has the duty to withhold Holy Communion. He adds, "Against Burke’s view and mine stand some scattered negative episcopal demurrals (Cardinals Roger Mahony, emeritus of Los Angeles, and Donald Wuerl of Washington, D.C., come to mind) and some short essays by academics." Here we have Catholics disagreeing in what seems to be good faith about a matter of public import; Mr. Peters, the canon lawyer, is going to argue his side from the text of canon law.
I think Mr. Peters puts his finger on the point of contention (at least among Catholics) here:
Participation in Holy Communion is achieved by two related but distinct acts: the action of a member of the faithful in seeking Communion (reception) and the action of the minister in giving Communion (administration). These two actions are not only performed by different persons, they are governed by different canon laws. Virtually all confusion over Communion can be traced to the failure to keep these two actions distinct.
Canon 915 governs administration; Canon 916 governs reception.
Mr. Peters makes a good case that, yes, ministers have a duty to withhold Communion from certain individuals under certain circumstances, and the highly publicized cases of Catholic politicians who are either living in irregular unions or fervent supporters of legalized abortion have largely fallen under these circumstances. But he also points out that the conditions under which Communion may be withheld are, indeed, narrow.
...[T]he conditions requiring Communion to be withheld must be simultaneously satisfied before the minister may licitly withhold the Eucharist from a Catholic approaching for it publicly. To invoke canon 915 [the conditions requiring Communion to be withheld] against a member of the faithful who does not satisfy all of the terms of canon 915 is....to disregard the plain text of the law and, as St. Thomas warned centuries ago, to violate the fundamental rights of the faithful.
....[I]f a member of the faithful approaches Communion publicly and gives no indication of intending an external act of desecration, even the minister’s moral certitude that the would-be recipient suffers grave moral disarray does not permit him to withhold Communion. His grief at being a material cooperator in sacrilege may be joined to our Lord’s grief at so many unworthy receptions of himself.
This is important because the public outcry against withholding Communion has often been along the lines of "Doesn't the Church know that everyone is a sinner? If they start withholding Communion from people who live in second marriages or have the 'wrong' political views now, maybe they'll withhold it for something else less serious next!"
It is important to be clear that the minister does not get to judge the entire conscience or conduct of the Catholic who approaches for Communion. The only judgment he gets to make is what is outlined in Canon 915. Ambiguous cases, Peters argues, "must be decided in favor of receiving the Sacrament."
One might argue that it is silly to stress the limitations of Canon 915 when, it seems, the problem we are living in is one of laxity, not overzealousness, in protecting the Sacrament from sacrilege and in protecting the faithful from scandal.
I think it is important, though, to point out that the rules, properly enforced, contain limitations which are meant to protect the right of the faithful to receive the sacrament. It is also scandalous to give the impression that bishops and pastors have the power to unilaterally and arbitrarily decide to withhold the sacrament. They do not.
That some of them appear to unilaterally and arbitrarily decide not to withhold the sacrament -- in situations with no ambiguity -- contributes to the impression of lawlessness. We would all be better off if we stuck to the text; it is there for a reason, in Catholic jurisprudence just as in civil jurisprudence.

I gave a quick answer for the combox:
I think it's a question worthy of highlighting for further discussion, don't you?
My point, in putting Roe v. Wade within a unit on the experience of childhood, is to point out that it affected the legal status of children primarily -- much more than it did the legal status of women. Of course, this only follows from the notion that unborn children are, in fact children; but I am sure the commenter understands that this is a fundamental assumption in my homeschool.
As with all my educational theories, we shall see how it plays out as my children get older and ask tougher questions. My philosophy about imparting the conviction that the unborn deserve protection is that it's necessary to go beyond "abortion is bad, so don't ever have one or pay for one or recommend one, try to help people who think it's their only choice, and vote against it whenever you can."
What's more fundamental than that? What's more necessary than that? Well -- ask yourself why abortion is a bad thing, why people shouldn't have them, pay for them, promote them, why it's better to help people make different choices, why its legal status should change. The only good answer is that the unborn are persons, children, and all those judgments follow from it.
The Catholic novelist and short-story master Flannery O'Connor once famously said about the Eucharist, "If it's just a symbol, then to hell with it." Well. About the anti-abortion movement, I can say: "If the unborn aren't persons, than to hell with it."
And so the thing that must be imparted is the gut-and-brain knowledge that unborn children are nothing more nor less than children, younger than themselves. A ten-year-old boy will protect his little sister like a Rottweiler: I have seen it. A four-year-old girl will carefully care for her baby brother: I have seen it. The whole family will gather eagerly around Mom's belly to watch for the tiny kicks: I have seen it. They know. They mustn't lose this knowledge.
If you know that an unborn child is a child, you don't need to be told that she needs care, not violence.
If you know that an unborn child is a child, you don't need to be told that a scared pregnant girl is a scared young mother with a baby, that a boy with a pregnant girlfriend is a worried young father. I'll have completely failed any one of my sons if he makes it to adulthood without being able to imagine what it might be like, what it is like for too many American men: to fear that he can't care for his family. I'll have failed my daughter if she grows up without putting herself in the place of a mother who's afraid she can't care adequately for herself and for her child.
I believe that to awaken compassion for young mothers and young fathers and their children is to awaken a desire to help them all, not a desire to harm any of them. Political positions come long after that.
Readers: What do you think of Emma's question and challenge? A good one, no?