30,000 denominations redux

I'd like to revisit a mindless but ever-popular Catholic trope about the Protestant faith. And that's the claim that sola scriptura spawned "30,000" denominations. The figures varies depending on the Catholic apologist. This is related to the Catholic objection that Protestants can't agree on anything. 

Here's why I say that's a mindless trope: if you think the Protestant movement is so disunited that it doesn't stand for anything, then why classify all these groups as Protestant? Put another way, if you can't say what the opposing position represents, then you have no target to aim at. 

If there's no such thing as a core Protestant theology, then there's nothing to critique. At best, a Catholic apologist could say the basic problem with the Protestant faith is that there is not Protestant faith. That would be catchy, and you could put it in one pithy sentence. 

But of course, Catholic apologists offer detailed critiques of Protestant theology. They write whole books on the subject. And Catholic attacks on the Protestant faith bear an uncanny family resemblance. 

In practice, a Catholic apologist takes one of two approaches. One line of attack is to critique generic Protestant theology. He attacks typical, representative Protestant doctrines. But that's a roundabout admission that Protestant faith does have a common, identifiable core theology.

The other line of attack is to pick a particular expression of the Protestant movement like Baptists, Presbyterians, Lutherans, or Calvinists. Although these have distinctive positions that distinguish them from one another, they are representative Protestant schools of thought. 

So both in principle and practice, Catholic apologists think there are recognizable Protestant doctrines. If they didn't think that, they couldn't write entire books attacking the Protestant faith.