“...by what or whose authority do you make judgments that they are wrong and not *real* Catholics, or *true* popes?...”
By the authority indicated in the comments of Pope Innocent III and Saint Robert Bellarmine below.
Pope Innocent III’s teaching:
“The pope should not flatter himself about his power, nor should he rashly glory in his honour and high estate, because the less he is judged by man, the more he is judged by God. Still the less can the Roman Pontiff glory, because he can be judged by men, or rather, can be shown to be already judged, if for example he should wither away into heresy, because he who does not believe is already judged. In such a case it should be said of him: ‘If salt should lose its savour, it is good for nothing but to be cast out and trampled under foot by men.’” [7]
Notice that he qualifies his statement by saying “or rather, can be shown to be already judged.”
A pope who is already judged is not pope, that’s why he can be judged. Bellarmine said just that:
Therefore, the true opinion is the fifth, according to which the Pope who is manifestly a heretic ceases by himself to be Pope and head, in the same way as he ceases to be a Christian and a member of the body of the Church; and for this reason he can be judged and punished by the Church.
When does Bellarmine say the pope loses office: This is the opinion of all the ancient Fathers, who teach that manifest heretics immediately lose all jurisdiction… NOT AFTER WARNINGS OR DECLARATION BECAUSE heretics already before being excommunicated are outside the Church and deprived of all jurisdiction. For they have already been condemned by their own sentence, as the Apostle teaches (Tit. 3:10-11), that is, they have been cut off from the body of the Church without excommunication, as St. Jerome affirms…
(De Romano Pontifici 30)
Full article:
https://stevensperay.wordpress.com/2016/01/23/st-robert-bellarmine-and-john-of-st-thomas-versus-john-salza-and-robert-siscoe/
Judged by WHOM?
And by WHAT criteria?
So it looks like it depends on if your favorite popes say so.
1.2 billion personal interpretations of Catholicism.
So, you and whose army will be marching into St. Peter’s Square and tossing Pope Francis and the Magesterium out??? As far as the WHOLE world knows, HE’S your leader until another is elected to take his place. Has the Holy Spirit confided in you as to when that will occur?
But it is fundamentally against Roman Catholicism for the likes of you to be the judge as to whether the pope is guilty of formal heresy based upon your understanding of what he taught, and whether Bellarmine was right versus Suarez, and whether that settles the matter.
I hardly think Bellarmine did not mean for for the likes of you to be the judge of who an invalid pope, which leads to every man a pope invalidator, nor it is your place to even authoritatively judge if Bellarmine was right.
In making private persons as yourself the judge of this based upon your understanding of your supreme authority, in essence you are as a Protestant, who judges the validity of claims based upon what his understanding of his supreme authority, and along with such you hold that Catholicism is largely in apostasy, with the bishops themselves over all not agreeing with your judgment.
That you are not fit to be judge of popes is clearly disallowed by historical RC teaching, as already showed you , with no response,
that .'the one duty of the multitude is to allow themselves to be led, and, like a docile flock, to follow the Pastors," "to suffer themselves to be guided and led in all things that touch upon faith or morals by the Holy Church of God through its Supreme Pastor the Roman Pontiff," "of submitting with docility to their judgment," with "no discussions regarding what he orders or demands, or up to what point obedience must go, and in what things he is to be obeyed... not only in person, but with letters and other public documents ;" and 'not limit the field in which he might and must exercise his authority, " for "obedience must not limit itself to matters which touch the faith: its sphere is much more vast: it extends to all matters which the episcopal power embraces," and not set up "some kind of opposition between one Pontiff and another. Those who, faced with two differing directives, reject the present one to hold to the past, are not giving proof of obedience to the authority which has the right and duty to guide them," "Nor must it be thought that what is expounded in Encyclical Letters does not of itself demand consent."
As regards the sixteenth-seventeenth century Jesuits Francisco Suarez and St. Robert Bellarmine, the former held (http://www.crisismagazine.com/2015/can-pope-heretic) that,
Catholics are supposed to believe that God deposes popes, then Scripture, the Tradition of the Church, and the pronouncements of the Magisterium ought to have said something about it—but they haven’t. Besides, if God deposes popes, you could never be sure if the pope was really the pope—what if he was a secret heretic and God had secretly deposed him? How would you ever know? (Suarez, De fide, 10.6.2-4)
But, if a pope commits the sin of heresy, all the other bishops of the world have the right to try him for the crime of heresy, even against his will (De fide 10.6.7). If they were to convict him, he could be considered deposed from the papacy by Christ, and the Church could elect another pope.
Yet which conflicts with such statenent as that in Dictatus papae [1075], attributed to of Pope Gregory VII, "That he himself may be judged by no one."
Meanwhile, Bellarmine held
that the pope loses his office immediately by committing the sin of formal heresy, because people who commit that sin cease to be members of the Church, and God deposes a pope who is no longer a member of the Church.
But Catholics are not to take it upon themselves to make that judgment, but the bishops would need to declare that God has removed the pope, but your sect no only has an invalid pope, but effectively renders the modern magisterium overall to be invalid.
Of course, the Catholic church distinctives are not only absent in the writings of the NT church ( Acts onward, which are interpretive of the gospels), but contrary to it.