One of the most interesting aspects of AVH's discussion was her account of opposition the beatification of Pope Paul VI. Apparently, she and Dietrich had told him, to his face and as a couple, that his failure to make the teaching of Humanae Vitae explicitly de fide had permitted great harm to come to the Church, especially to the credibility of her teaching authority. I agree. That, combined with his butchering of the Roman Rite, actually visited great harm on the Church. The effects are very much with us. While Montini personally was both orthodox and humble, his policies were generally disastrous.
The disaster consists in what is a de facto, three-way schism in the Church today. On the "Left" we have the progressives, whom I call "progs" for short, and on the "Right" we have the traditionalists, often called "rad-trads." (The political categories of left and right are only an analogy, but often apply literally to individuals; thus the majority of progs are political leftists and the majority of trads political rightists, though there are notable exceptions because the underlying categories of ecclesial politics far transcend those of secular politics.) As Fr. Richard John Neuhaus of First Things has pointed out, progs and trads agree that Vatican II represented a decisive break in the story of the Church, so that we may now speak in effect of a new Church discontinuous with the old one. The main difference between them is that the progs think the new Church is a good thing and want her to become newer still; the rad-trads think she's a bad thing and want her to recover her lost virtue. Neuhaus calls progs and trads respectively the left and right "branches of the party of discontinuity." (The article of his I've linked above appears, in slightly revised form, as a chapter in his trenchant new book Catholic Matters, which I highly recommend to everybody for whom the Catholic Church matters.)
In the "Center" are the continuants, called "neocons" by progs and trads. They think the post-Vatican-II Church is the same Church as before, needing today only a "reform of the reform." The best representatives of the Center, the continuant party, are of course popes John Paul II and Benedict XVI. The truly loyal Catholics are those who follow them. But among active Catholics, it cannot be taken for granted that the Center is the majority. The progs who do not believe what the Church has always taught, and the trads who believe that the Church no longer teaches what the Church had always taught before, are together at least as numerous. The majority are not in formal schism, but refuse to have anything to do with each other and, for good as well as bad reasons, are most dissatisfied with the current hierarchy. While a few trad groups have long been in formal schism with Rome, a small but growing number of prog groups are now too, founding churches presided over by ex-Catholic priests and a few women who have been "ordained" for the purpose. To the trads, the loyalists are the Left; to the progs, the loyalists are the Right. The loyalists caught between such extreme viewpoints considers themselves just—well, Catholics.
This mess has come about because of Paul VI's mistakes. John Paul II tried to deal with the de facto schism in various ways, many of them quite impressive. His encyclicals alone—even aside from his media stardom and evangelizing travels—are sometimes breathtaking. But he failed to impose discipline on many of the clergy and, by extension, imposed almost none on the laity. Perhaps he and the present pope are waiting for demographics to do slowly what confrontation would do quickly. For obvious reasons, the progs don't produce many babies or priests, and the trads only have only so many sympathetic bishops to accommodate them. In the meantime those senior loyalists who, like Alice von Hildebrand, remember the old days as the good old days can only pray for the next generation.