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.

Hey guys can we stay on topic please

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. 

A true Pope is not prevented by the Holy Spirit from making errors in disciplinary matters or prudential matters in general.

You fail to make a distinction.  Indeed, the Pope is prevented by the Holy Spirit from making errors in disciplinary matters that affect the entire Church.  This has been the result of many decades of SSPX gaslighting and denying the disciplinary infallibility of the Church.

It is absolutely false that a legiitmate Pope can promulgate a form of Public Worship, and Rite of the Holy Sacrifice of the Mass, that is offensive to God and harmful to souls.  It is also absolutely false that the Pope can make errors in matters such as canonizations and in the general Canon Law of the Universal Church, even if he can make errors in laws affecting certain parts of the Church or certain individuals.

A true Pope is prevented by the Holy Spirit from teaching actual "heresies," as the Church defines the term. A true Pope is not prevented by the Holy Spirit from making errors in disciplinary matters or prudential matters in general.