While the Pecknold essay linked here has to do specifically with Covid 'vaccines,' the principles of "common good" noted by the author extend far beyond that debate. It's not some vacuous 'moral imperative' as some (even Bishops) would have it. It actually requires rational analysis.
...The only way out is through—to a more ancient view of the common good, which turns on a more classical understanding of justice and the character of law itself. In his Treatise on Law, Thomas Aquinas states a basic precept that cuts to the heart of the matter: “Laws framed by man are either just or unjust. If they be just, they have the power of binding in conscience, from the eternal law whence they are derived.” Aquinas would certainly reject the libertarian refusal of mandates in principle, and would agree with the liberal that the public authority can mandate vaccinations. Aquinas teaches that the state can compel and bind conscience in law, but that there are limits, or if you prefer, conditions which limit this. He gives three specific conditions: Laws are just when, first, the reasons for the law are ordered to the end of everyone’s flourishing; when, second, they do not exceed the legitimate power of the legislator; and when, third, such laws do not lay unreasonable burdens on subjects. Citing Augustine’s dictum, “an unjust law is no law at all,” Aquinas insists that the legislator’s power is legitimated precisely through an appeal to the reason and end of the law. Are the burdens imposed reasonable for all? Do they really serve the ends to which they are ordered?...
...We know that our Covid-19 vaccines are effective at reducing the chance of infection, and may reduce the severity of symptoms. But we also know something else about our Covid vaccines: Unlike the mandatory polio vaccine, Covid vaccines will not eradicate Covid. Does this mean they fail the reasonableness test? Not necessarily, but it is the sort of question that is clearly oriented to the end of the flourishing of the commons while avoiding the typical, emotional abuse of the common good we saw in Silas House’s Atlantic essay or in Biden’s unnecessary and counter-productive mandate.
An example of those thinking in light of a reasonableness test is a recent statement by the Vatican’s chief doctrinal office encouraging everyone at risk to get vaccinated, but which recognized that forced medical procedures must meet a high bar of necessity to count as a reasonable burden. The Vatican did not rejects vaccination mandates in the way a libertarian might, because they recognized that it might actually be necessary and reasonable to mandate vaccines, as it was with polio. This counsel is rooted in a proper, true understanding of the common good. States can indeed bind consciences—the liberal is right about this, and the libertarian is wrong—but only by agreed means of discerning what actually is true and just, and not simply by capricious and unnecessary compulsion. Neither legislators nor laws can bind consciences on the basis of power alone.
This is why many are now advocating for civil disobedience, not because they are lawless, selfish, or are enemies of the common good, but because they think the law isn’t rational, and isn’t necessary. If laws are not demonstrably just, if they cause undue burdens without end, if they exceed the due power of legislators, if they do not accord with reason or even basic facts, then they cannot bind the conscience because no authority can justly compel obedience irrationally.
That "common good" platitude is used and abused regularly by Progressives; it's their claim to moral liceity on all sorts of issues, not the least of which is the Current Hotness, CRT/DEI.
It's a trap. Insist on rational argument; in all likelihood, they can't provide it.