I am rather puzzled by the application of the “Neocon” label to what seems to be a liberal Catholic. I would think that it would mean “more conservative” than typically conservative, who are in fact “moderates” that want to abide, not change.
Were I to apply the label of “Neocon” to a Catholic group, I would think their agenda would include such things as a “Counter-Reformation” against liberal heterodoxy and pagan heresy in the Americas. Even so far as to call on the Vatican to create an instructional mission, for several religious orders to observe and correct such error where found in each diocese, under the authority of the Holy Office.
I use quotes around the word "religious" above because First Things is notoriously non-religious in many respects . . . at least in terms of its watered-down approach to religious subjects.
A Neo-Conservative Catholic is a Catholic with a total disdain for the Catholic liturgical and social-doctrinal past from prior to 1962, and a glaring ignorance of Catholic dogmatics between the Patristic era and 1950, but who is unstintingly Orthodox, Loyal, and Ultramontanist as far as the recent Vatican positions formulated in the past 45 years. Its a very Ignatian/Jesuitical position, where the key measure of Catholicism is unswerving devotion to the latest papal utterance.