1: Francis is the Pope, Vatican II was a council that was ambiguously worded, that can (perhaps only with difficulty) be reconciled with tradition, but is too easy to interpret in a manner contrary to tradition (hence why a lot of people are doing so.)
2: Francis is the Pope, but Vatican II is a "pastoral" council that isn't meant to be infallible. While normally even non-infallible acts of the magisterium would be given serious weight, in this case the council can't be reconciled with tradition, so those points of the council must be rejected, EVEN IF it means being out of regular communion, "we must obey God rather than man."
3: Vatican II was a false council, and whether it claimed infallibility or not, Francis and the other conciliar popes are in fact not true popes. Thus nobody needs to be in communion with him/them.
First off, buckets 1 and 2 can be combined because they are basically the same. V2 was never meant to be infallible, which the hierarchy of new-rome has admitted multiple times over the last 5 decades. Therefore, since it's not infallble, it's possible to be wrong. The term "pastoral" is a novel term and didn't exist 50 years ago, so you can substitute "pastoral" for "fallible" and the theological weight of V2 becomes more clear.
Secondly, being "in communion with rome" is another novel term which has only been in use since V2 times. What does it even mean? No one knows for sure. It's a modernist term which is meant to imply that person/group x is not "friends/obedient" to new-rome, while ignoring the reasons why the obedience is not given. It is an emotional phrase which plays upon a catholic's innate nature to trust the pope and hierarchy, which is why V2 was successful to begin with - because too many sheeple accepted an easier, less-extreme Church, while using the excuse of "obedience" to calm their consciences.
Bucket 3 is really a combo of 2 different ideas which are not connected at all. V2 was a false council and it did not claim infallibility. This has no bearing on the status of the pope, which is a separate question. It certainly has no bearing on any of the post-V2 popes (i.e. JPII, Benedict, Francis) because they didn't have anything to do with the V2 documents, so how can their status as pope be effected by something which happened before they were elected? It can't.
It seems to me that if #2 was true, one should want to be in communion with Francis (since he is, in fact, the Vicar of Christ on earth) so long as doing so does not obligate one to accept Vatican II.
All Traditional Catholics are in communion with Eternal Rome and with 1,950 years of 250+ popes. Being "in communion with" (again, whatever that means) the last 4-5 popes of the V2 era only matters if these popes are orthodox. Our Catholic Faith is built on dogma, doctrine and Truth. The salvation of our souls depends on the Faith, not on the pope, who can lose his Faith and go to hell like the rest of us. Our obligation is to be "in communion with" the Truth, not the pope. If the pope teaches the Truth, then we are correctly to place ourselves under his authority, not because of his title, but only because he is following Christ, from which all authority originates. Any pope who deviates from Christ and the Truth has no authority, for no one can command another to sin or to accept error, even the pope.
The V2 popes will always obligate those "in communion with" them to accept V2/new mass because this is their new religion. There has been not one former-Trad group who has joined new-rome who has been allowed to reject V2/new mass and the new-sspx will not be an exception. When the new-sspx joins new-rome, they will be an indult community exactly like the FSSP, which has compromised their Faith, and offered their pinch of incense to the new world religion, in exchange for being "one of the gang" and for being "in communion with" heretics.
It *seems to me* (as someone who I admit is not an expert on the various positions and issues) that the SSPX wants communion with Rome, but on condition that they don't have to accept all of Vatican II. Whereas it seems to me that the SSPX Resistance doesn't want any communion with the Pope at all, while still saying he's the Pope.
Again, the new-sspx will have to accept V2 and the new mass. They might be allowed to question this or that aspect of V2 but they will NOT be allowed to criticize the new mass, which is much more of a problem/scandal/blasphemy than is V2. The new mass is the culmination of V2 and is the essence of modernism. You can reject the entire council of V2 but if you accept the new mass, you've lost your soul.
I can see how that former position could be not schismatic? How is the latter one?
The V2 church is who is in schism because they have deviated from 2,000 years of orthodoxy, they promote a "mass" which is anti-Council of Trent, anti-sacrificial in nature, anti-Catholic in purpose. For the last 50 years, we've not had a true pope (in the sense that they were orthodox, and maybe they were not pope at all?), so the issue of schism is secondary and really, irrelevant due to the chaos in the Church. When all of us die who live during this period, Our Lord will not ask us if we were schismatic or not. He will ask us if we kept the Faith and protected the Truth. You can only be in schism if you separate yourself from an orthodox pope.
Yet if the pope is not orthodox, then to separate from him in an effort to save your soul is NOT schsimatic but heroic, prudent and catholic.