The thesis of this critical essay is most clearly articulated toward the middle of the essay: 

Monsignor is chiefly important because of what he represents about Amory and Amory’s relationship with the ancient European literary, cultural, and religious tradition. 

For much of the essay, the suggestion is that Monsignor Darcy is a symbolic figure for Amory. Darcy represents, for Amory, a father figure first and primarily. Secondarily Darcy represents a connection between Amory and 1) the past, 2) certain artistic and cultural ideas. (This idea can be taken as another way to phrase the essay's thesis). 

Monsignor advises him on what to read, whom to idealize (“some such man as Leonardo da Vinci,” for example), and which philosophies to follow.

In turning away from Darcy, Amory establishes his individuality. This independence occurs on several levels, according to the essay. For Amory, this is an independence driven by egotism in which the character denies the value of tradition. For the people of Amory's generation, the split from the past has larger ramifications:

Monsignor and Amory’s relationship is a metaphor for the relationship between Europe and the United States before and after World War I. 

Casting the priest as the rejected father, Fitzgerald offers a rebuke not only to the artistic traditions of Europe but to the wider European cultural traditions that defined its civilization for centuries. 

But Fitzgerald envisioned something even more extensive than a break with Europe’s politics and literary tradition; he very purposefully uses the image of a Catholic priest to represent the separation and, therefore, firmly connects it to a rejection of this faith.

It is at this point that the essay directly connects the notion of religion to the characters in the novel, arguing that Amory's relationship with Darcy can be understood as a symbol for Amory's spiritual state (which is intimately related to his cultural and artistic state).