I have no knowledge beyond what wiki has told me today. FWIW wiki asserts there are tens to hundreds of thousands of adherents to some variation of sedevacantism. In a ~1 billion member church, even 100,000 is a very small percentage. But it’s vastly more than “a couple dozen”.
I was being a little sarcastic when I said “dozens,” and actually I was referring to those who believe that Cardinal Siri was elected Pope, not John XXIII. But still, I’m surprised. I would have thought the Lefebvrists (the Society of St. Pius X) might have a few thousand adherents. But the sedevacantists? I’m amazed that there are that many. I’ll have to look at the Wiki article and see what its sources are.
I guess if you add up every Catholic who is upset by the vernacular Mass and other post-Vatican II reforms, you might come up with tens of thousands, or even 100,000. But those are the traditionalists, the Latin Mass types, who are not necessarily sedevacantists.
Again, I am surprised.
Faster than light, that’s for sure. Somebody once said that whenever light arrives the darkness is already there waiting for it.
Even as a heathen 
, you might be interested in Andrew Greeley’s book, “The Making of the Popes 1978.” It’s a fascinating study of electoral politics in the College of Cardinals in the elections of JP I and JP II.
Fascinating stuff about the sedevacantists, Northern Piper, and your info on Formosus, Captain Amazing, lived up to your surname.
BTW I didn’t really expect that they would erase Popes from the historical records in Stalin fashion, but I did wonder how Catholic theologians reconciled a Pope like John XII being elected with the doctrine of the College of Cardinals being infused by the Holy Spirit to guide them in their choice of Pope. It seems unlikely that a member of the Trinity would goof but perhaps to err is divine as well as human. 
The traditional answer is that God has to act through humans, and sometimes humans do not listen to God, or consciously disobey God. That’s what Original Sin is about.
But the traditional answer is also that no matter how fallible the humans in the church may be (or even in extreme cases, actually evil), God will not let the Church fall for ever.
Yes, Tolkien was very Catholic - why do you ask?
OP variant with ex-post-facto declared “bad” Bishops:
,
Along these lines, and its doctrinal argument/position reduced to its simplest form, was at the root as a discreet case in Catholic doctrine, after assuming political form–was the bishop consecrated by a sinning bishop a faithful executor and bona fide bishop–and exponentiated to one of the most challenging heresies of the early Church: Donatism and its various, sometimes armed sects in the fourth and fifth centuries. It essentially separated the North African community from the Roman one permanently, despite the impassioned efforts of St. Augustine backing up the papal thunderbolts and those of Constantine himself, equally under threat from the schismatics.
Short story, from a current-day source of Catholic apologia.
Slightly longer, but with cites, story, from Wiki.
Long story, from The Catholic Encyclopedia.
Pterry, IIRC.
Bolding mine. Discrete. As a logophile you surely appreciate the significance of the difference.
Not at all. It’s obviously -C
Here’s the Perfect Master on some of the bad Popes (after discussing the supposed “Pope Joan”): Was there once a female pope? - The Straight Dope
I’ve always been very disappointed that the story of a special chair for new Popes after Pope Joan was a myth. The story was that the elected Pope would sit in the chair, which had a hole in the seat, and each Cardinal would come along, feel the Pope’s testicles, and declare, Testiculos habet et bene pendentes, which loosely translated is, He has balls and they hang well. As the Italians say, se non è vero, è ben trovato, even if it isn’t true it’s a great yarn!
Apparently the chair was real, but its actual function was different from what the legend says. And actually, it seems to have been three chairs: one “commode”-type seat, and two porphyry “pierced” chairs.
Above comes from Christianity.stackexchange.com
Well, the sedevacantists are a kinda side issue, since they dont think the "not a pope Popes’ were Bad, just that the sedevacantists didnt like their politics.
As a Catholic, I find the word “Un-Pope” to be wholly inappropriate.
How about “Depontificate?” Or “Depapify”?
I was kind of wondering about that too. Not that it’s inappropriate one way or another, but what, if any, the word is in Catholic discipline.
Similarly, un-Bishop and down the line. Is “defrock” a term of art?
I think the phrase you are liking for is “Byeshop”.
As a non-Catholic I too found it unsatisfactory. I just couldn’t quickly come up with an alternative. Retroactively unseat may have been a better, if clunkier, term.
The Master Speaks:
Nice typo.
This sounds, and is, wrong, if ultimately true (i.e. more than truthy, but less than helpful): the thunderbolts came from…Constantinople.