What, or who, do these people think they are fighting? A Jesuit priest, Fr. Roger Haight, had a book of his (from 1999) censured by the Congregation for the Doctrine of the Faith (CDF) four years ago, in December of 2004. In his theological work Jesus: Symbol of God, Fr. Haight put forth several ideas about who Jesus Christ is, what the Trinity is, and whether Jesus Christ is the unique savior of the world; these ideas attempt to redefine Christology in a way that the CDF considers unreconcilable with the Catholic faith. You can read about it in their notification on his book.
The seven primary points which the CDF says Fr. Haight calls into question are 1) the theological method, 2) the pre-existence of the Word, 3) the divinity of Jesus, 4) the Holy Trinity, 5) the salvific value of the death of Jesus, 6) the unicity and universality of the salvific mediation of Jesus and of the Church, and 7) the Resurrection of Jesus. These are weighty issues! They are central to the whole teaching of the Church!
The "these people" I refer to in my link to the National Catholic Reporter (a source every Catholic should utterly avoid, excluding John Allen's column which is its sole Catholic perspective) are the people who claim in their comments that "Rome" is afraid of losing its power by having this priest question "Rome's" doctrines. It is as if just before Vatican II, "Rome" got together and defined Jesus' divinity, the Trinity, etc., and Vatican II was meant to free Catholics from such stuffy ways of thinking (as if God favored any one religion, one person says).
These people are evidently not aware that these doctrines were hashed out in the early centuries of the Church. And it was not "Rome" (as these people imagine it to be) that made these definitions, it was a Council of Bishops. One person actually attempts to contrast "the teachings of the Second Vatican Council" with the doctrines being questioned by Fr. Haight, saying that Vatican II's teachings "could actually be considered as definitive because of our Bishops meeting in a sacred Council". Where does he come up with this stuff? What of the sacred Council of Nicea? What of Ephesus? Does he know where the Catholic faith comes from? It comes to us from the Apostles, and through the Magisterium of the Church. It is defined and clarified through sacred Councils.
What did Vatican II say about Jesus' divinity, the truth of the Holy Trinity, the pre-existence of the Word, etc.? Long story short, they reaffirmed the Church's tradition teaching and theology. It wasn't concerned with challenging or changing any of these things; it's not in the Church's power to do so! Read Lumen Gentium 14-17 and see what the Church teaches about Christ as the Savior of the world. Read Lumen Gentium 22 and see what the Church teaches about the Pope as the supreme pastor of the Church.
How do people choose to remain this ignorant?! It appalls me.