Sorry about dropping off. I've been extremely busy the past few days.
SedeDoubtism is actually pretty straightforward. I consider the legitimacy of the Vatican II popes to be in doubt.
I find this to be by far the most preferable attitude towards the current crisis. Unfortunately, Traditional Catholics have become polarized and radicalized into the sedeplenist and sedevacantist camps so that more and more we find dogmatic sedevacantists and dogmatic sedeplenists.
By adopting sededoubtism I avoid formal schism because my reason for refusing submission is based on objective, material, positive doubt about their legitimacy. If I happen to be wrong and Francis I is the pope, then I would be in material but not formal schism. I also avoid the damage done to the authority of the Church's magisterium by the magisterium-sifting mentality. I also avoid the damage done to the Church's infallibility and indefectibility.
By adopting sededoubtism I also avoid the schismatic attitude often found among sedevacantists of considering any person in the Novus Ordo or any non-sedevacantist to be schismatic. I also defer to the Church's authority by recognizing that mine is only a private opinion and does not suffice to make definitive judgment on a matter that has to be known with the certainty of faith (legitimacy of popes is in the category of dogmatic fact) ... thereby avoiding the damage done to the authority of the Church's magisterium by the pope-sifting mentality.
It allows us to stay in an attitude of humility and avoid schismatic tendencies. We can therefore go about the work of saving our souls in peace and tranquility and without bitter zeal. In one way it's a humble "punt" of the entire issue.
If I were a priest, for instance, I would offer the Mass "una cuм famulo tuo papa nostro" but would leave out the actual name. On the one hand I profess submission to the Supreme Pontiff in principle, and to Francis conditionally (in the event that he happens to be the Pope) but I wouldn't risk positively affirming allegiance to an AntiPope and thereby introducing an infamous name into the Sacred Canon.
With this position, there's no impediment to Traditional Catholics of varying opinions to begin working together in mutual charity and in humility. I found all the other positions to be seriously problematic.
When I have more time this evening, I'll get back to illustrating the problem with outright sedevacantism from the perspective of the Church's authority and the harm it does to the magisterium and to the Church's authority. I think that the problem of potential schism in radical sedeplenism is pretty straightforward.
What's funny is that I think both sides are RIGHT and that both sides are at the same time WRONG. In other words, sedevacantists have some very valid criticisms of the sedeplenist position. On the other side, sedeplenists have some very valid criticisms and concerns regarding the sedevacantist position.
Consequently, I adopt a sededoubtist position which in fact concedes the valid arguments on both sides of the issue without presuming to necessarily "solve" the problem. To my mind that belongs to people at a "higher pay grade" than mine, so to speak. I'm just trying to save my soul, keep the faith, and not offend God or do any harm to the Church.
Obviously this is all within the context of Traditional Catholicism. Of course the alternative would be something in the Novus Ordo continuum or spectrum (from full-blown acceptance to Indultism (aka extraordinary formism) to FSSPism to Fellayism...which is right on the border).