One is either schismatic or not.
Correct. And per Pope Bl. Pius IX, who defined Papal Infallibility and Primacy of Jurisdiction, in Quartus Supra, "But the neo-schismatics say that it was not a case of doctrine but of discipline, so the name and prerogatives of Catholics cannot be denied to those who object. Our Constitution Reversurus, published on July 12, 1867,[23] answers this objection. We do not doubt that you know well how vain and worthless this evasion is. For
the Catholic Church has always regarded as schismatic those who obstinately oppose the lawful prelates of the Church and in particular, the Chief Shepherd of all. Schismatics avoid carrying out their orders and even deny their very rank.Since the faction from Armenia is like this, they are schismatics even if they had not yet been condemned as such by Apostolic authority. For the Church consists of the people in union with the priest, and the flock following its shepherd.[24] Consequently the bishop is in the Church and the Church in the bishop, and whoever is not with the bishop is not in the Church."
https://www.papalencyclicals.net/pius09/p9quartu.htmHello. The above underlined is classic Recognize and Resist.
Not in the sense the neo-schismatics mean it. Certainly, liberalism is to be refused e.g. a false liberal Vatican Ostpolitik with Chinese Communists today, that greatly endangers Chinese Catholics, and is not for the good of the Catholic Church. That can and should be refused. There are good Cardinals and Bishops who are doing that.
It is a completely different matter to rashly break off complete communion with the Pope and the Bishops; for, those who withdraw from Catholic Communion, will gradually perceive all their works and prayers grow cold, because they do not share in the benefits and blessings of the Unity of the Catholic Church, as the Council of Florence teaches us: "The Most Holy Roman Church firmly believes, professes and preaches that all those who are outside the catholic church, not only pagans but also ... schismatics, cannot share in eternal life and will go into the everlasting fire which was prepared for the devil and his angels, unless they are joined to the catholic church before the end of their lives; that
the unity of the ecclesiastical body is of such importance that only for those who abide in it do the church's sacraments contribute to salvation and do fasts, almsgiving and other works of piety and practices of the Christian militia produce eternal rewards; and that nobody can be saved, no matter how much he has given away in alms and even if he has shed his blood in the name of Christ, unless
he has persevered in the bosom and the Unity of the Catholic Church." We must examine our conscience in its light. If you don't believe me, that's up to you. But this is infallible Church Teaching.
I did not say that the SSPX are not considered to be Catholics
Well, at least you acknowledge that. And that is enough to refute your absurd opinion, because any Catholic is allowed to belong to or support a Catholic Fraternity. But what you ought to do is confess the sin of sede-vacantism, or sede-doubtism, or sede-whateverism, and ask your Priest to be reconciled to the Catholic Church, with firm resolve not to fall back into it. As Bp. Fellay mentioned, "As a result of the Pope’s act, during the Holy Year, we will have ordinary jurisdiction. In the image I mentioned, this has the effect of giving us the official insignia of firefighters, whereas such a status was denied us for decades."
https://damselofthefaith.wordpress.com/2015/12/01/ordinary-jurisdiction-for-the-year-of-mercy-bishop-fellay-says/ the SSPX is not only Catholic but also Her Bishops have Ordinary Jurisdiction going ahead, so the objection is refuted. One ought to be subject to Catholic Bishops who have Ordinary Jurisdiction and it's perfectly Catholic to be such, sede-doubtist subjective absurdities aside.
Here's Pope Boniface VIII in Unam Sanctam, "Furthermore, we declare, we proclaim, we define that it is
absolutely necessary for salvation that every human creature be subject to the Roman Pontiff." There's no exception that says "if you personally believe he's not the Pope, then it's not necessary". And as Fr. Hunter says, if the Bishops are united in recognizing a certain man as Pope, they are certainly right, for otherwise the Body of the Bishops would be separated from their Head, and the divine constitution of the Church would be ruined. The Church defects. In other words, sede-ism denies the indefectibility of the Teaching Church. Read about Eastern Catholic Martyrs who died under Communist Terrorism to remain faithful to the Roman Catholic Church, and in no way break from Catholic Unity with Rome, the Mother Church, even though being much pressured and persecuted to do so; and you will see how foolish it is to risk your spiritual growth and jeopardize your salvation by living unlike Roman Catholics have always lived, i.e. more or less out of communion with Rome. Modern sede-ism practically denies the indefectibility of the Roman Church which Fr. Fenton also spoke of. Both SVism and "R&R" as commonly used are mistaken. The True Traditional Catholic position is refusing liberalism while remaining in communion with the Teaching Church, which is indefectible, and with the Roman Church, which is also indefectible.