How are you Catholics any more doctrinally united or harmonious than we Protestants? You have your radical feminists, hyperconservatives, New Agers, and everything else, just like we do. And among born-again, Bible-believing Evangelicals there is unity, just as there is among traditional Catholics.
It is true that one may find people who believe anything—or nothing—and who call themselves “Catholic” or “Protestant.” These labels do not, by themselves, establish unity. Nevertheless, the Catholic rule of faith confers doctrinal unity in a way that the Protestant rule of faith does not.
The Catholic rule of faith is “the Word of God in Scripture and Tradition as understood by the Church”; the Protestant rule of faith is “Scripture alone.” Although there are those on both sides (radical feminists, New Agers, etc.) who have no regard for either rule of faith, who heed neither Scripture nor the Church, the difference is among those who do.
While the mere claim to be “Catholic” doesn’t necessarily tell us much about a person’s belief, the claim to follow the Catholic rule of faith, to believe the teachings of Scripture and Tradition as defined by the living Catholic magisterium, does. But the claim to follow the Protestant rule of faith, to believe the teachings of Scripture alone, hardly tells us more than the claim to be “Protestant.” One could be Baptist or pedobaptist, Calvinist or Arminian, Anglo-Catholic or low-church Anglican or anything in between.