Preliminary Note: This is not the only case of error out there. I could probably write a logic text using nothing but examples from anti-Francis Catholics to demonstrate bad reasoning. But it is an error that undermines trust in the Church and needs to be addressed by itself.
The problem is, under that line of reasoning, it indicts every Pope since St. Peter, and overlooks the fact that societies sometimes have vicious customs—evil acts commonly accepted in a society despite the teaching of the Church. For example, the French and their infamous acceptance of mistresses despite the fact that the Church has consistently condemned adultery and concubinage. If the current widespread sins of Catholics “proves” the approval or incompetence of the magisterium, then it also follows that the Church is to blame for not stopping mistressing. St. Paul VI (Humanae Vitae) is to blame for the acceptance of contraception among Catholics, and St. John Paul II (consistent warnings against the culture of death) for the prevalence of abortion. Never mind that they and their successors fought these evils and urged Catholics to reject and oppose them.
Even if one only speaks about corruption among the clergy (where there’s even less of an excuse for ignorance), you can’t say that it could only exist because of approval or indifference of Rome? St. Peter Damian wrote “The Book of Gommorah” (epistle 31) about the practice of homosexuality in monasteries and urging reform. Popes did take action to reform these evils but the evil did not vanish. Are we to condemn every Pope from Leo IX forward for this fact? Abortion was condemned since the first century but some Catholics still support it. In other words, this argument aimed at accusing one Pope or one Council would actually indict all of them if the widespread existence of a sin is the fault of a Pope.
This attitude is effectively a re-emergence of Pelagianism, believing that one is able to overcome sin through their own efforts. This re-emergence assumes that the Pope just has to make a harsh enough statement and Catholics will obey. We should consider what Pope Francis had to say in Gaudete et Exsultate:
49. Those who yield to this pelagian or semi-pelagian mindset, even though they speak warmly of God’s grace, “ultimately trust only in their own powers and feel superior to others because they observe certain rules or remain intransigently faithful to a particular Catholic style.” When some of them tell the weak that all things can be accomplished with God’s grace, deep down they tend to give the idea that all things are possible by the human will, as if it were something pure, perfect, all-powerful, to which grace is then added. They fail to realize that “not everyone can do everything,” and that in this life human weaknesses are not healed completely and once for all by grace. In every case, as Saint Augustine taught, God commands you to do what you can and to ask for what you cannot, and indeed to pray to him humbly: “Grant what you command, and command what you will.”
Some things are beyond human effort and, if God’s permissive Will allows them to remain, we will not be able to overturn them no matter how much we want to (cf. Numbers 14:39-45).
This doesn’t mean “do nothing.” It means each age has its own evils and we must work to overcome them, relying on the grace of God to strengthen us for the task. Not by accusing people of malfeasance if the results are different than we want.