Ross Douthat's (in)famous tweet encouraged those who find themselves advocating positions that the Church has consistently rejected to "own" their heresy.
As he has explained, not all liberals are heretics, and not all liberal Catholic ideas are heresy, but a significant element of Catholic liberals seem to think that pretty much everything (aside from the Creed and maybe some clearly infallible core of later councils and papal teaching) is up for grabs. And this is clearly heresy.
While John Paul II and Benedict XVI worked vigorously against this heresy, for whatever reason--most likely fear of making division within the Church worse--they didn't name it as heresy.
But what heresy is it? Is it just modernism redux? It it even a single heresy? Many of have claimed (plausibly) that "modernism" doesn't really describe an actual heresy or coherent school of thought. And, when you look at the condemnations from Pius IX and Pius X, it does seem to be kind of grab-bag of modern ideas or attempts to modernize the Church.
And, of course, the heresy that goes under the name of liberalism is similar. There's not one identifiable, consistent error or line of reasoning that defines it. It is rather--like modernism--defined by its desire to fully reconcile the Church to the times, and it's pretty much willing to throw any line of reasoning at that project that will stick.
So, in a sense, whatever common thread--however thin--joined together the ideas that got condemned as "modernism" in the nineteenth century, it could be argued that contemporary liberal Catholicism (in its more radical forms, at least), shares that thread, even if its particular claims and ideas aren't identical with those of the nineteenth century modernists.
As both traditionalists and liberals like to point out, at least some of the ideas once condemned as modernism seemed to have been adopted by Vatican II (and, actually, to some extent, before that). Traditionalists point this out to condemn the council and the popes since John XXIII as modernist heretics. Liberals point this out in order to claim that the Church changed her mind about modernism.
There's obviously some truth in this. There was, at least, a moderate appropriation of certain ideas that were once condemned with modernism, such as historical-critical study of the Scriptures, and acceptance of democratic forms of civic government and religious freedom. Likewise, the idea of aggiornamento is an acceptance that the Church--to some degree at least--can and should be reconciled to the modern world.
Still, the official line and intent of the Council and the popes has not been an embrace of modernism, but a kind of moderate and flexible response to modernity that seeks to distinguish what is essential, internal, and unchangeable and from what is non-essential, external, and changeable. An adaptation of approach, but not a wholesale reevaluation of Catholic teaching or practice.
I'm sympathetic to a traditionalist critique that views that approach to be naive and, in some ways, wrongheaded. At least when it comes to actual human beings rather than intellectual abstractions, there is no "mere" external that you can modify without affecting in some way the internal. The reform of the liturgy has, in fact, changed the faith, despite the benign intentions of Paul VI. (I won't speak of whether the intentions of the liturgical reformers were benign.)
Even so, it remains that the Church did not accept the core premise or project of modernism. While the Church did acknowledge that there is a hierarchy of truth--with essential and more certain things at the center and less essential and certain things at the peripheries--it has, to this point, maintained that the standard of truth and reform comes from within that hierarchy--not from the world.
And this, perhaps, is the key distinction between genuine reform and adaptation to the times and heresy of modernism/liberalism. The latter believes that the modern world is to be set up as judge over the faith and not vice versa.
