In the past, conservatives prided themselves on loyalty to the pope and being in lockstep with all papal teachings, while progressives called for limits to papal power.
The devotees of tradition used to argue that liberals who complained about papal infallibility or centralization were backsliders who really needed to get with the program.
So while the John Paul II and Benedict XVI papacies had liberal theologians arguing that popes should govern more collaboratively, traditionalist critics of the current pope "have become reluctant to accept papal teaching (in its contents and forms) only with Francis," said Villanova University theology professor Massimo Faggioli.
In the recently published book "To Change the Church," Ross Douthat compares Francis to President Trump, arguing the pope is seeking to push through changes without thinking about the consequences.
Faggioli says the tradition of the Catholic Church in defining papal authority is "conservative," in the sense of being cautious.
"The extremist interpretations of papal primacy and infallibility have been rejected both by Vatican I and the post-Vatican I Church," he said. "It is healthy that Catholics see limits in papal powers."
The decision to host the cardinal is significant given that the archbishop of Philadelphia, Charles Chaput, leads the United States bishops' committee on "laity, marriage, family life and youth," which has a remit to implement the teachings in "Amoris Laetitia."
The Archdiocese of Philadelphia did not respond to requests for comment about Burke's attendance at the cathedral event or whether this meant the archbishop was endorsing the cardinal's position.
For his part, Chaput has issued guidelines to his archdiocese on "Amoris Laetitia" stressing that remarried Catholics can only receive Communion if they are living as "brother and sister," and he recently described Douthat's book as an "intelligent and absorbing work."
And while his cathedral is hosting a cardinal who is threatening to correct the pope, the archbishop steered clear of a conference on Francis' papacy that took place near Philadelphia at Villanova University on April 12-15 and brought together some of Francis' closest confidants and advisers. The pope himself met with the university's president and trustees in the Vatican while the Villanova conference was in full swing.
Finding themselves criticizing a pope may, in the long run, see conservatives end up with a more nuanced and balanced view of papal authority. In the meantime, liberal Catholics could offer them a simple message: "Welcome to the club."