A lot of people in the Novus Ordo (especially very conservative and red-pilled N.O.'s) just don't want their pride hurt, as well as an exodus from their social circle. They know deep down at this time what the truth is... The patterns are there, the proof is there, it's just burying their head in the sand at this point..

This isn't 1985 any more. The revelation is clear as mud. 

There also seems to be an attachment to lukewarmness in the N.O. It's kind of unwritten dogma of the N.O. to be lukewarm, or your a kook. Any one feel simialr?

So ... that's an incredibly tenuous distinction.  To be subject to the "Papacy" in some abstract form reduces to little more than lip service.  There must be a concrete expression and manfiestation of that to THIS pope.  There's actually some condemned proposition out there about separating the office and the office holder.

Where the line has always been drawn is between the Pope acting as Pope, i.e. exercising his office v.s the Pope acting as private person or private theologian or Pope acting as pastor or Pope acting as bishop of Rome.  In the former case, he must be intending to teach the entire Church or to impose some discipline on the entire Church.  In other cases, he might just be giving a Sunday sermon to those in his chapel, opining on the papal plane, giving interviews to Scalfari, or making some changes to how the Diocese of Rome works.  But when he addresses a teaching to the Universal Church, typically the demarcation has been in an Encyclical Letter or above ... where it's clearly addressed to the entire Church, not when he's giving a long-winded speculative speech to a group of midwives (as the dogmatic SVs have exaggerated infallibility to include).

With such teachings, addressing the Universal Church, religious assent is required, but religious assent has been misdefined and misunderstood as being tantamount to internally believing as if it were infallible truth, every such teaching that does not meet the notes of infallibility ... making it so that the SVs have effectively made every sentence in Pius XII's Allocution to Midwives become for all intents and purposes the same as a Solemn Dogmatic Definition.

That's because both sides are missing the forest for the trees, arguing about strict infallibility when it's more about broader indefectibility ... and infallible safety.  R&R reduce the protection of the Holy Ghost over papal teaching to a handful of dogmas, and the rest can turn to complete garbage ... whereas SVs counter by claiming that pretty much every time the pope passes wind (even if not from his mouth), he's infallible.  While the SVs claim to follow pre-V2 teaching, they cannot cite a single theologian who extends infallibility as far as they do.  So the quibbling goes on.

Where the line is draw is that ... if you find that you must sever Communion with the hierarchy because you don't even feel that they have the same religion you do, where you realize that in order to remain a faithful Catholic and save your soul, you must refuse submission to that hierarchy, its teaching, and its Public Worship ... as well as to its law / universal discipline, and ignore the vast majority of their "saints" (and their cultus) ... that line has been crossed where that's clearly contrary to the Promises of Christ to protect the Papacy.  Period.  Now, you could try to make various assertions about how maybe they're blackmailed or "suspended" due to heresy, or lacking formal authority, or just non-popes simpliciter due to Siri (my position) ... but there's no reason to throw out Christ's Promises for the Papacy just to avoid this eeeeevil of sedevacantism.  As I said, you could even avoid SVism if you hate it that bad by claiming that these popes are blackmailed and not acting freely.  I doubt it's true, but you would not be trying to keep the faith ... by throwing the very core of it under the bus to save the Modernists.

Yes, the purpose of the True Pope is to uphold the True Faith. His purpose is to insure that Catholic does not "defect from the Faith." By following the true Roman Pontiff's teachings, we are assured of that our Faith will be an indefectible Faith. He is a means to an end. He is not the end itself. Keeping the Faith and Obeying God is the ultimate end.

Here is the key quote from Pastor Aeternus that says that:

6. For the Holy Spirit was promised to the successors of Peter not so that they might, by his revelation, make known some new doctrine, but that, by his assistance, they might religiously guard and faithfully expound the revelation or deposit of faith transmitted by the apostles. Indeed, their apostolic teaching was embraced by all the venerable fathers and reverenced and followed by all the holy orthodox doctors, for they knew very well that this See of St. Peter always remains unblemished by any error, in accordance with the divine promise of our Lord and Savior to the prince of his disciples: "I have prayed for you that your faith may not fail; and when you have turned again, strengthen your brethren."

7. This gift of truth and never-failing faith was therefore divinely conferred on Peter and his successors in this See so that they might discharge their exalted office for the salvation of all, and so that the whole flock of Christ might be kept away by them from the poisonous food of error and be nourished with the sustenance of heavenly doctrine. Thus the tendency to schism is removed and the whole Church is preserved in unity, and, resting on its foundation, can stand firm against the gates of hell.

Again, we don't worship the true Papacy or the true Church for its own sake. They are both the means of Salvation precisely because they were instituted by Christ to keep us on the right path. We follow a papal claimant as long as he "religiously guards and faithfully expounds" the True Faith. If a papal claimant introduces "new doctrine," then we can be sure that he is not the the true Pope.

But as Ladislaus said, there is a tendency with many traditionalists to think that every statement of a papal claimant must be held to be infallible and if he says something that sounds "new" then he is a "heretic." That is the root of everyone's disagreements. Not all errors are heresies. And judging a papal claimant to not be a "heretic" because he has erred in some prudential matter is the reason for many of the disagreements.

Hey guys can we stay on topic please

Sorry, bud.  It looks like everyone forgot about you.

6. For the Holy Spirit was promised to the successors of Peter not so that they might, by his revelation, make known some new doctrine, but that, by his assistance, they might religiously guard and faithfully expound the revelation or deposit of faith transmitted by the apostles.

  If a papal claimant introduces "new doctrine," then we can be sure that he is not the the true Pope. 

No Angelus, what we can be absolutely sure of, per your quote from V1 in your item #6 above, is that there is no Divine Protection if/when the pope preaches a "new doctrine"i.e. heresy. We are certain of this because that's what it says.

Also per #6, as long as the pope is guarding and expounding Catholic truths, the Holy Ghost assists him. Which is to say that there is no divine assistance at all if/when popes preach new doctrines or promulgate errors.

What it does not say, imply, or otherwise suggest anywhere, is  that a true pope cannot preach new doctrines i.e. heresies, or that a pope cannot *not* safeguard Catholic truths.