God has revealed that before the "coming of Our Lord Jesus Christ" he would permit a "son of perdition" to sit in the Temple of God. Many have speculated that this will be someone sitting on the seat of Peter as pope. This revelation indicates that this will "please" God.

Stubborn is right about temptation and purification being in God's plan, even evil and heretical popes. The only other "son of perdition" in Scripture is Judas, a betrayer among the very apostles. The use of the term to apply to the final Anti-Christ suggests that he will be a pope, or a bishop arrogating the powers of the same.

It is also willed that the faithful oppose him, and flee the "abomination of desolation" - and all resisters here, R & R, Sedes - all who are Traditional Catholics - do so.

Good answer, can't argue with that.

God permitted this atrocity as part of our chastisement.

Agreed. Our Lady warned us of this several times, most notably at La Salette and Fatima, even as far back as Quito. While I don't think we've had a legitimate pope since Pius XII, I do think it is just and true for God to allow men to fall into their sins and suffer the consequences. In this case, be deceived by a counterfeit church and hierarchy. Men began to run after worldliness and their passions once the ʀɛʋօʟutιօn hit France and the so-called "Enlightenment" swept the world. We were warned, we deserved it, and God gave it to us. Many so-called Catholics today have no interest in the truth, and for that are being swept up in this torrent of heresy and apostasy.
St. Paul predicted it when he spoke of the last days:

For the mystery of iniquity already worketh; only that he who now holdeth, do hold, until he be taken out of the way. And then that wicked one shall be revealed whom the Lord Jesus shall kill with the spirit of his mouth; and shall destroy with the brightness of his coming, him, Whose coming is according to the working of Satan, in all power, and signs, and lying wonders,And in all seduction of iniquity to them that perish; because they receive not the love of the truth, that they might be saved. Therefore God shall send them the operation of error, to believe lying: That all may be judged who have not believed the truth, but have consented to iniquity. - 2 Thess. 2:7-11