Pope Francis did indeed demote Cardinal Raymond Leo Burke, as the piece notes. In the parlance of the Roman Catholic Church, cardinals are referred to as princes in the church's hierarchy. Cardinals are also bishops. In the church's hierarchy, the pecking order is bishop, archbishop, cardinal. Like most monarchs throughout history, Pope Francis does not like to have his own views criticized publicly by a courtier at the Vatican, as Cardinal Burke had done.
As Daily Kos notes, Cardinal Burke's strident cultural-warrior views are shared by a number of other bishops in the United States. In addition, a certain number of lay American Catholic reactionaries hold strident cultural-warrior views as well. See Damon Linker's book THE THEOCONS: SECULAR AMERICA UNDER SIEGE (2006).
However, if you want to succeed as a discrete and prudent courtier at the Vatican, you should study the seventeenth-century Spanish Jesuit Baltasar Gracian's book THE POCKET ORACLE AND ART OF PRUDENCE, translated by Jeremy Robbins of the University of Edinburgh (Penguin Classics, 2011; orig. ed., 1647). I have no reason to suspect that Pope Francis read Gracian's book, but it is possible that he may have read it. However, it is far more likely that Pope Francis, the first Jesuit pope, learned in effect how to embody the spirit of Gracian's advice in that book by studying the life and example of St. Ignatius Loyola, the founder of the Jesuit religious order in the Roman Catholic Church that is known by the informal name as the Jesuit order (also known by the formal name as the Society of Jesus).
Progressives and liberals might cheer on Pope Francis when he inveighs against economic inequality. In addition, they might welcome his announced upcoming encyclical of climate change.
But Pope Francis appears to be a media darling still. In part, this is due to his off-the-cuff comments at times, which the journalists covering him dutifully report. Oftentimes, his reported extemporaneous comments do not seem scripted. On the contrary, they seem spontaneously and refreshing.
For example, his comment "Who am I to judge?" was widely reported -- and itself widely commented on. He made this comment in response to a hypothetical question about a homosexual possibly serving as a Roman Catholic priest.
In light of the Roman Catholic bishops' opposition to same-sex marriage, which Pope Francis is also on record as opposing, his comment seems almost "off-message" (as we say when a politician says something that does not seem to be the usual, scripted message we would expect to hear).
Clearly Pope Francis can hold to his position of opposing same-sex marriage, on the one hand, and say, on the other hand, "Who am I to judge?" regarding the hypothetical case of a homosexual possibly serving as an ordained Roman Catholic priest. In effect, Pope Francis's comment shows that he can walk and chew gum at the same time, as we say.
However, Pope Francis is decidedly conservative regarding established positions taken by the Roman Catholic bishops. As a result, he is not likely to initiate any significant changes in established positions. But because of his ability to walk and chew gum at the same time, he may continue to come across as something less than a fervent cultural warrior regarding the established positions that he is not likely to change.
Of course Pope Francis is the first Jesuit ever elected to serve as pope. As noted, the Jesuit religious order in the Roman Catholic Church was founded by St. Ignatius Loyola. In a relatively short time, the comparatively well-educated Jesuits were being characterized pejoratively as being "Jesuitical" by certain detractors.
Historically, the Jesuits adopted the approach known as moral Probabilism in their practice of being confessors for the faithful. Their Probalism contended with the more legalistic medieval approach known as Tutiorism. No doubt the Jesuit use of Probabilism as confessors also contributed to their detractors' use of the term Jesuitical in a pejorative sense. See Robert Aleksander Maryks' book SAINT CICERO AND THE JESUITS: THE INFLUENCE OF THE LIBERAL ARTS ON THE ADOPTION OF MORAL PROBABALISM (2008).
Incidentally, in six of his 112 learned endnotes, Robbins mentions Cicero in connection with various points that Gracian discusses.
In theory, however, the term "Jesuitical" could also be used in a non-pejorative sense as a positive characterization of certain typical tendencies or behaviors of Jesuits. After all, the quip about not being able to walk and chew gum at the same time can be turned into a positive quip by saying that somebody (e.g., Pope Francis) can walk and chew gum at the same time.
So if the pejorative descriptor "Jesuitical" can also be used in a non-pejorative way, we might wonder what the non-pejorative way of using "Jesuitical" might mean beyond the obvious sense of meaning "like a Jesuit." For example, we might wonder if Pope Francis is Jesuitical beyond the obvious sense of meaning "like a Jesuit." In other words, can we amplify a bit about what it may mean to be like a Jesuit?
Because the term "Jesuit" is an informal name for the religious order, we should note that the order's more formal name is the Society of Jesus. Therefore, first and foremost, to be a Jesuit means to be like Jesus. Thus the non-pejorative meaning of Jesuitical should mean "like Jesus."