Schism is defined as "cutting oneself off from the Mystical Body of Christ" or considering non-Catholic that which is Catholic.
For purposes of this discussion, I'm not talking about the Pope.
In fact, for the sake of discussion, let's assume that the Pope is a manifest heretic, and someone convinces me that it is necessary for a layman to openly treat him as a non-pope. The whole, "I'm not judging or deposing the Pope, I'm just using common sense that a manifest heretic can't be Pope..."
Ok, so for purposes of discussion, let's grant that the man Cardinal Bergoglio is not Pope.
Now FROM WHAT PIT OF HELL do so many sedevacantists get this idea that everyone in the Novus Ordo is not Catholic? That no priest is priest, that no bishop is bishop, and that no layman is Catholic? That is nothing more or less than schism. If you accidentally lopped off even a dozen true Catholics, you've just taken a knife to the Mystical Body of Christ, which is the textbook definition of Schism. Sorry, you can't do that.
I have been a Traditional Catholic all my life. I know what Tradition is about -- it's about staying aloof from the official Church structures and authorities, which has been overwhelmingly taken over by Modernism and Modernist ideas. The Faith itself is being lost all over world -- by clerics and laity alike. Souls are being lost, that might have otherwise been saved. In a World War, many souls were saved that would have otherwise been lost. (Think: men on the battlefield who might have died in mortal sin during peacetime, but instead they went to Mass, confession, etc. from a Catholic chaplain and then died in battle that day) See why Vatican II was a worse Chastisement than the previous two World Wars?
But if it's true that this or that bishop, this or that cardinal, this or that priest, and this or that layman has clearly lost the Faith -- or is losing it -- it's also true that many still have the Faith. Not because of the Novus Ordo Missae and the new religion, but in spite of it. Because of TAN Books reprinting pre-V2 Catholic books. Because of this or that priest choosing to keep the Faith. Because of accidental adhesion to pre-V2 devotional practices. Because of a personal prayer life, and so on.
An order of nuns dedicated to adoring the Blessed Sacrament would be one such example. Can you say that "all novus ordo nuns aren't nuns" just because they're not affiliated with the CMRI, or they don't get involved in controversy? What does it mean to have the Faith, anyhow? I'd say worshipping Christ hidden in the Blessed Sacrament is one of those signs that you still have the Faith. Let's be real: no one without the Faith is tempted to worship a circle of bread. Unless you BELIEVE that it is the Real Presence of Christ, you would not give up a "normal life", family of your own, etc. to spend hours worshipping such.
That's exactly what you have in the case of the convent where Our Lady of Akita made her appearance. And yet how many Catholics would be tempted to dismiss the whole thing, just because it wasn't a CMRI or SSPX convent? How many Sedevacantists are misnamed -- they're actually Ecclesiavacantists. They're about an "Empty Church" rather than an "Empty Chair".
How can so many so-called Traditional Catholics be so comfortable with excommunicating 1 billion Catholics? It's not about the Pope. The Pope is a separate issue. Even if I grant that you can "declare the Pope deposed" or whatever you want to call it, it doesn't extend to every Catholic, to every vestige of Church authority. Has the Conciliar Church shut down, ceased to exist? Where is Authority then? With the handful of Trad bishops? Even if that's your belief, then I ask you: which of them is competent to rule in a case like Akita? I would say that the local bishop still has a Bishop's authority, AT LEAST until he himself proves to be a manifest heretic. And saying a dangerous Mass is not enough to render one a vitandus ("to be avoided" public heretic who has lost any office. He can still have the Faith, even if he says a Mass that tends to destroy the Faith. It just isn't a smart idea, that's all.
I think too many Trads have a "cooties" mentality with regards to the Novus Ordo. They like the idea of throwing out the whole ball o' wax and starting over. Nice and simple; nice and clean. Well, I'm not for easy OR for simple. I know that usually an easy solution is the wrong one.
At any rate, we need to judge just judgment, not cultivate a cult or schismatic mentality.