Civility, yes, but fairness and accuracy too
Consider their principle no. 2: "As lay Catholics we should not exhort the Church to condemn our political opponents by publicly denying them Holy Communion based on public dissent from Church teachings. An individual's fitness to receive communion is his or her personal responsibility. And it is a bishop's responsibility to set for his diocese the guidelines for administering communion."
First, I wonder why the CACG aims this advice only at lay Catholics? Does the CACG consider priests and religious not bound by the rules of civility? Or, do they think that priests and religious have more rights than laity to express their views in this area? If so, I suggest the CACG consult, to choose only one of about a dozen relevant norms here, Canon 212 upholding the right of all the faithful to express their views on matters affecting the good of the Church. Supposing, though, that the CACG does not hold with either conclusion, one wonders why they expressed themselves so clumsily as to even raise the question. Still, there is more wrong here than poor phrasing.
It is a common ploy of political discourse to distort another's position and then demolish the caricature hoping that observers will conclude that, whatever the other side held, it must have been wrong. The CACG does this when it portrays those who support the withholding of Communion from certain politicians as if they support the Eucharist being withheld from "political opponents" per se, instead of, as is really the case, from those who "obstinately persist in manifest grave sin" (1983 CIC 915). The CACG wants readers to conclude that, because no one should support withholding the Eucharist based only on political differences, the practice of withholding the Eucharist from political figures must be wrong. Indeed, the CACG describes this action as "condemning" political adversaries, making those who support some withholding of Communion appear especially ruthless. These are, I think, grave distortions of the real issues and, if I may say so, they constitute very uncivil ways to portray those who disagree with the CACG.
The CACG seems completely unaware of the important distinction between public and private responsibility in the administration and reception of Communion when it asserts: "An individual's fitness to receive communion is his or her personal responsibility." But, as so many writers in so many fora have noted (e.g., here, here, here) the observance of Canon 915 (that binds ministers in the public arena) is at issue here, not Canon 916 (that binds individual members of the faithful in conscience). I cannot imagine a group that claims to be making a credible contribution to this vital discussion not even alluding to, let alone reckoning with, this key distinction. The CACG does neither.
Finally, despite having stated (more or less accurately) that "it is a bishop's responsibility to set for his diocese the guidelines for administering [C]ommunion", cannot the CACG see that some bishops have concluded that certain people's activities (albeit in the political sphere) constitute, under Canon 915, a disqualification for reception of the Eucharist in their diocese (that is, as far as these bishops' responsibility for the Eucharist extends)? What exactly, then, is the CACG's complaint against these bishops, except that that the CACG (resting on shoddy argumentation) disagrees with their decision?
There are, I'm afraid, additional problems with other CACG assertions, but the above comments should suffice to show that one's laudable willingness to urge the observance of civility in public debate is not necessarily a measure of one's impartiality in that debate, or even of one's ability to discuss the issues raised in those debates accurately.
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Other reactions: Catholic World News, Mark Brumley, Catholic Family and Human Rights Institute, Carl Olson, Robert Miller