At some point in history, and this was long before Vatican II, bishops simply stopped excommunicating people for heresy. For a few hundred years after the Protestant Revolt against the Church, declaring an excommunication wasn't really necessary since individuals who broke from the Church refused any association with the Church and publicly condemned the Church as being of the devil. Heretics stopped claiming that they were reforming the Church and instead declared that they were founding (or re-founding) the actual church they said they believed Christ really founded. Thus, they, themselves, called their church Lutheran, Anglican, Presbyterian, etc., etc., etc.
In some respects, the Catholic Church entered into a survival mode. The bishops no longer had to formally excommunicate anyone because the heretics refused any association or communion with them. The bishops, and even the popes, became complaisant. Anyone who claimed to be Catholic was accepted by the bishops and the popes as Catholic. As time progressed, the Holy Office would condemn the writings of a person as heretical, require changes or suppression of the texts, but the individual writer himself was not required the repent and, oftentimes, continued in his heresy.
Even Pope St. Pius X merely warned us about the Modernists. He did not expel them from the Church if they did not repent of their heresy. For the first time in history (at least as far as I can determine) since the Arian Crisis, people, particularly priests and theologians, could remain "in communion" and in good standing with the Church even though they had become Protestant simply because they did not personally declare themselves to be founders or members of a different religion but, instead, claimed to still be Catholic.
Thus, in spite of the fact that the Council of Trent had formally declared Truths of the Faith and all who denied them were anathema--that is, outside the Church--the hierarchy became loathe to enforce the anathema on actual individuals. This has brought us to the very problem we have today. Catholics in general, even traditional Catholics, even sedevacantist in many cases, simply will not refuse communion with almost anyone who says he's Catholic even when the individual directly denies, in word or deed, the Catholic Faith.
In addition to the problem above, most of Western society has succuмbed to Fɾҽҽmαsσɳɾყ which declares that all religions are equal. Also, one of the "errors of Russia", that mutually exclusive statements can be true is deeply ingrained upon the Western mind. Thus, many people will continue to accept the proposition that men who knowingly deny a truth of the faith in word or deed are still Catholic.
So, Myrna, few people will deny the title of Catholic to anyone who himself claims the title, Modernism having permeated the Conciliar Church through and through.