So you're an Anti Semite, too? You people are insane.

She was simply agreeing with my sentiment that you have the right to self-identify without being judged.

note the pope says, "[f]or that reason, they additionally deny the indefectibility." What reason? The one he just stated: they say the pope and the bishops in union with him in an ecuмenical council declared heresy.

If you assume that "for that reason" / "therefore" / "consequently" refers to the previous sentence only, then you're right. But if you read it to refer to the three previous sentences, to what Pius IX says from the beginning of the paragraph, number 22, about the "Old Catholics", then the fact that they have "constituted a pseudo-bishop" is part of their actions which consequently imply denial of the indefectibility of the Church.

The gist of the paragraph then is:

They constituted a pseudo-bishop, attack and pervert the true power of jurisdiction and transfer it to the people, obstinately reject and oppose the infallible magisterium, boldly affirm that the Church fell into heresy, consequently, they also deny the indefectibility by declaring that the the Church has perished and the restoration of a legitimate episcopacy is neccessary.

22. And surely what these sons of perdition intend is quite clear from their other writings, especially that impious and most imprudent one which has only recently been published by the person whom they recently constituted as a pseudo-bishop. For these writings attack and pervert the true power of jurisdiction of the Roman Pontiff and the bishops, who are the successors of blessed Peter and the apostles; they transfer it instead to the people, or, as they say, to the community. They obstinately reject and oppose the infallible magisterium both of the Roman Pontiff and of the whole Church in teaching matters. Incredibly, they boldly affirm that the Roman Pontiff and all the bishops, the priests and the people conjoined with him in the unity of faith and communion fell into heresy when they approved and professed the definitions of the Ecuмenical Vatican Council. Therefore they deny also the indefectibility of the Church and blasphemously declare that it has perished throughout the world and that its visible Head and the bishops have erred. They assert the necessity of restoring a legitimate episcopacy in the person of their pseudo-bishop, who has entered not by the gate but from elsewhere like a thief or robber and calls the damnation of Christ upon his head.

We can't make ourselves a rule of law above the Church and its governance. Leo XIII and Pius IX seem to have confirmed this in Satis Cognitum, with the essential government of the Church tied to the Roman See, and the idea that the head of the Church and all the bishops tied to it via the apostolic see defected is blasphemous. Again, you've explained how you disagree, but I simply don't find your points convincing. Agreeing to disagree is fine.

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Well, everyone does this in one way or another, since we all reject the heresies of Bergoglio (except Poche). And that's on private judgment, not on the judgment of anyone else. Where you want to go with that idea determines which traditionalist camp you fall into.
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Even if you want to say that this only maintains until the consummation of the world, it seems extremely harsh to say that this is clearly the consummation of the world. Says who? The interpretation of a few people, most of whom are certainly wrong about other forms of doctrine, about a problematic council? There are certainly still interpretations of Vatican II that don't fall into objective heresy, much less formal heresy. If someone believes that they shouldn't go to mass to avoid perceived heresy, then I can't fault them for following their conscience. The problem instead arises when people say that those who do go to mass without any actual intent of heresy or wrongdoing will go to Hell or are separated from the Church, when this is clearly not true.

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You give a lot of attention to whether or not other people are allowed to say what they are saying. I find this a little odd. If you disagree with something someone else says, why not just ignore it and consider it nonsense? Why does it bother you so much if other people disagree with you? And along similar lines, you seem to also be bothered greatly to try to determine the subjective state of other people's consciences. This comes out more in your next paragraph:
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If it is the case, then Struthio is the only person on this thread doing the right thing, and everyone else's case is mere vanity. In fact, with the exception of him and maybe truecatholics.org, everyone else is going to Hell.

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Why not just leave it to God to figure out things like this?
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But as Ladislaus has said numerous times on numerous different threads (and which I will readapt here), even if rejecting an opinion is objectively heretical, this doesn't mean the person rejecting it is a heretic.

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Yes, I say the same. Most trads of whatever variety say the same. This is nearly a universal belief in the trad world.
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Given my experience in traditionalist Catholicism, I tend to assume that people believe those who disagree with their specific opinions are formally heretical and doomed to damnation. Again, this attitude paints and taints a lot of conversations I have with traditionalists (especially the CMRI types).

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Jerm, can you please try an experiment? Next time you are having one of the conversations you describe here, just ask the person straight out the following question: "Do you believe that everyone on the other side of this question is going to hell?" For example, if you are talking to a sedevacantist, say, "Do you believe that everyone who goes to an SSPX chapel will go to Hell for heresy?" If you are talking to an SSPX person, say, "So do you believe that every sedevacantist will go to Hell for schism?" I think you will be very surprised at the answers you will get from doing this. I strongly doubt you will find even one traditional Catholic of any variety who will answer that question with a simple "Yes." If you do, please respond back and describe that conversation in detail.

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Well, everyone does this in one way or another, since we all reject the heresies of Bergoglio (except Poche). And that's on private judgment, not on the judgment of anyone else. Where you want to go with that idea determines which traditionalist camp you fall into.
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You give a lot of attention to whether or not other people are allowed to say what they are saying. I find this a little odd. If you disagree with something someone else says, why not just ignore it and consider it nonsense? Why does it bother you so much if other people disagree with you? And along similar lines, you seem to also be bothered greatly to try to determine the subjective state of other people's consciences. This comes out more in your next paragraph:
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Why not just leave it to God to figure out things like this?
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Yes, I say the same. Most trads of whatever variety say the same. This is nearly a universal belief in the trad world.
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Jerm, can you please try an experiment? Next time you are having one of the conversations you describe here, just ask the person straight out the following question: "Do you believe that everyone on the other side of this question is going to hell?" For example, if you are talking to a sedevacantist, say, "Do you believe that everyone who goes to an SSPX chapel will go to Hell for heresy?" If you are talking to an SSPX person, say, "So do you believe that every sedevacantist will go to Hell for schism?" I think you will be very surprised at the answers you will get from doing this. I strongly doubt you will find even one traditional Catholic of any variety who will answer that question with a simple "Yes." If you do, please respond back and describe that conversation in detail.

Sure, I will oblige! 
1) I talked to Fr. Desposito on the phone on September 16, 2019. When I asked him, directly, if I could continue to see Fr. Ringrose at St. Athanasius in Vienna, VA, he directly said to me that I could not. He told me that not only was it a sin to go to a priest who included Francis in the una cuм part of the mass, but you couldn't even go to a priest who was willing to work with priests who did so, under pain of mortal sin. He told me instead to go to confession once a year to a sedevacantist priest completely and utterly separated from an una cuм mass. 
2) I talked to Introibo ad Altare Dei, the popular sedevacantist blogger, extensively. At one point, I considered going back into union with Rome for the many reasons I've put up here. On December 15, 2019, he sent me this message: 
"I’ll pray for you as always Jeremy. One last piece of advice: If you’re right and I’m wrong, there’s no reason to worry. The Visible Head of Your Church has said: “Proselytism is solemn nonsense” and “There is no Catholic God.” So no worries! (Of course SSPX will strain all credulity by claiming “nuances” whereby “Proselytism is solemn nonsense” REALLY MEANS “outside the Church no salvation”)

If I’m right and you’re wrong—oh boy! Think of it as a modern Paschal’s wager.

God Bless,

—-Introibo"

If this isn't clear, I don't know what will be. As a note, he had told me it was okay to go to the SSPX before, but that any actual union with Rome will cause me to be damned. Still, not the best outlook.

3) As I have shared here before, I also was in correspondence with the popular Steven Speray for a while. I've noted his posts here claiming that even those who disagreed with the use of the 1955 Holy Week missal, such as Fr. Cekada, were on the path to Hell. I never directly asked him about this, but he always seemed to imply that those who disagreed with him, especially on BoD, would go to Hell and were outside of the faith. You can look at his blog to verify any of this.

4) At one point, I was considering being a layman connected to MHFM. They always tell everyone that all outside of their small, correct theology, will go to Hell, and that all who disagree with them are bad-willed heretics. It was no different with me. I do not have a direct citation for this one.

5) I also got in touch with the Home Aloner website truecatholics.org at some point, though I've since deleted the email. On their website, they directly stated that only Catholics who do not attend a public Mass can be considered as true Catholics. The website has actually since been deleted, as has their Twitter account.

Perhaps you can see why one would become scrupulous about this, when they are first looking into traditionalism, seeing so many different sources that they will go to Hell for going to the traditionalist Church closest to them (Fr. Desposito), going to Church at all (truecatholics.org), disagreeing with sedevacantism (MHFM), or even assenting to people like Fr. Cekada's (and therefore Fr. Desposito's) teachings on the 1955 Holy Week missal! At the time, I did not even know this forum existed, my entire family wasn't Catholic, and I had no traditionalist Catholic friends in real life. (I still don't, but I digress.) What is one supposed to do? How am I supposed to know who is right in this case, and how am I supposed to assume that Struthio isn't a dogmatic Home Aloner when every Home Aloner I've ever met said you would go to Hell unless you were a Home Aloner too?

As for me trying to read peoples' consciences, I had no intention of doing this. Nor am I trying to say people can't say their opinions, or that they're not allowed to have them. It does bother me when people try to say that their own opinions are dogma because, as a complete newcomer who just discovered traditional Catholicism about a year ago, how am I supposed to know that they're wrong? For example, I can think Struthio's perspective is wrong all I want, but as an already scrupulous person, how am I supposed to know that what I'm doing will save me? Ignorance won't save me either, so say so many people, so clearly I have to learn and discuss it with them, else I risk being damned. This is the way I used to think, and the way that I fear is still right today even when I technically know better. So, essentially, I had no one in my life to talk about this with, no way to figure out who was right, and I couldn't go to my priest nor Church out of fear of going to Hell for doing the wrong thing. And, even if I tried to do the right thing, I could never know it was right, and trying to do the right thing wouldn't matter at all because I would just be damned for it anyways. Don't you see why this would make someone upset?

I know that my posts can be annoying. In fact, most people would probably just prefer I shut my trap and stop posting. I know that I can be mean spirited. But I would appreciate some understanding of my situation by someone. Simply saying that I've done everything wrong for the past year isn't very helpful, and saying that I should sit down, shut up, and stop asking questions isn't helpful either. I want to find the truth, just like everyone else, and it's extremely difficult to do so when so many people are telling you completely contradictory things, and frequently, towards the beginning of my search, saying that you need to agree with them or you'll burn in Hell for eternity.

jerm, instead of clouding your mind with the various brands of dogmatism, you can simplify the problem by just asking whether dogmatism itself is correct.

Dogmatism outside of actual defined dogmas is not Catholic.  If you were to deny the Immaculate Conception, for instance, then you're certainly a heretic and outside the Church.

If, however, you apply Catholic dogma concretely to the crisis, you are using human reason and are capable of being mistaken.  But these are known as material errors.

Dogmatists do not understand the concept of material errors.

Formal heresy means a rejection implicitly of the AUTHORITY of the Church to teach dogmas.  Only those heresies which implicitly reject the actual authority of the Church to teach are formal errors.  No dogmatist, despite however good a syllogism he thinks he has derived from dogma, has the authority to claim that their conclusions are dogma.

If you acknowledge the Church's teaching authority and intend with your will to believe everything the Church has defined, then you are not guilty of heresy.  No one is counted as a formal heretic for drawing an erroneous conclusion from dogma.  Here's a good litmus test for having the faith.  If we were living at a time of an undisputed Pope, and the Pope came out and defined a dogma, would you believe it without question?  Would you believe it without reservation even if prior to that time you would have considered the opinion to be wrong?

Fr. Desposito was not my only example. When I talked to Home Aloners like those who made truecatholics.org (which, having searched a bit more, seems to have been merged with betrayedcatholics.org), they said you had to stay home from masses to be Catholic. Having not met a Home Alone Catholic who did not say this, and seeing you promoted the position, I assumed that you also thought you had to stay home to be Catholic at all, and that everyone who didn't would be damned for certain.
I am sorry if I misjudged you. If I'm wrong about your perspective, please tell me.

I am none of those either. I left Juda, went to the mountains, and I don't go where they say "here is Christ". But I am well aware that I have no mandate to command others. All men at all times everywhere have to form their conscience and follow it, says St. Thomas Aquinas.

I agree with this nowadays. However, I don't know if it's a simple question of whether dogmatism is right or not. To some, the question of dogmatism is a question of whether you're in the true faith or not. So, while someone associated with the remnant of Catholics who is wrong would be a formal heretic, a person in, say, the Novus Ordo who's trying to live a good Catholic life would not be. They would be no different than a mere savage Indian who did not possess the faith, and their ignorance would not save them.
This is the problem. A lot of the people out there who profess to be of the true Catholic faith believe in doctrines that are mutually exclusive from others. So, Bp. Sanborn and the CMRI say that those who don't agree with BoD are non-Catholic. The Novus Ordo says that those who don't recognize the Pope are non-Catholic. MHFM says that both are non-Catholics, and they're the only true Catholics. Many Home Aloners say that none of those groups are Catholic, but only they are. But, a lot of these ideas seem to also hold to different faiths than others. MHFM and Home Aloners seem to profess belief in a Church that can lose actual Apostolicity, which is different from the Creed, and government + communion, which is different from what the Popes of the past have said. This is the fundamental problem I have talked about.
With one's private judgment, even a nondisputed Pope could become a disputed Pope the second that he declared something dogma. If you believed that the Immaculate Conception was a heresy and the Pope declared it to be one, what would stop you from saying that he was simply a heretic and therefore a non-Pope? You could say that he's not a disputed Pope, but then, someone who rejects what the Pope says could just claim him to be one. It seems like the whole Catholic system dies if private judgments are valid.

It has been like this ever since. St. John, in his letter, talks about Antichrists even in his time. There have been all sorts of sects all the time in the past 2000 years. Consequently you will need some private judgment to use the brains the Lord provided you with to make up your mind.

[5] For many will come in my name saying, I am Christ: and they will seduce many.
[11] And many false prophets shall rise, and shall seduce many.
[12] And because iniquity hath abounded, the charity of many shall grow cold.
[23] Then if any man shall say to you: Lo here is Christ, or there, do not believe him.
[24] For there shall arise false Christs and false prophets, and shall shew great signs and wonders, insomuch as to deceive (if possible) even the elect.
[26] If therefore they shall say to you: Behold he is in the desert, go ye not out: Behold he is in the closets, believe it not.