Though the Novus Ordo, or Conciliar Church, is not Catholic, there are still Catholics in the Novus Ordo. Many (if not most) traditional Catholics were themselves, at one time, Novus Ordo Catholics; that is, Catholics in faith, believing that the Novus Ordo was the Catholic Church, trying to reconcile the obvious contradictions, learning the faith from others who still had the faith and from the older books and catechisms, searching for the Truth until, oftentimes quite by accident, they stumble upon tradition.
Few, if any, traditional chapels, orders, or communities, require people who find them to formally "convert" as they would a Protestant.
This is because the Church is still in the early stages of the Modernist Crisis. Because the scope is so big, it will take a very long time before all Catholicism is drained from the Novus Ordo. These times can be likened to the days in Elizabethan England when one's childhood parish slowly became Anglican instead of Catholic. And because the transition occurred over time and at different rates throughout England, it took a lot of time before one could finally declare that all Anglican churches and Anglican faithful were not Catholic.
We still cannot say that for sure of the Novus Ordo. There are a few Catholic priests (though they are in the beginning stages of corruption since they willingly participate in the Novus Ordo) and some Catholic faithful.
I think that the final break will come when the Vatican officially permits the ordination of women (which, I believe, will come) or some other critical event. Perhaps the Vatican will authorize intercommunion with Lutherans for the 500th anniversary of Wittenburg. There are signs of impending doom throughout the Conciliar establishment. The time will come, and I think it will be fairly soon, when no traditional Catholic will be able to give the benefit of the doubt to any Conciliar Catholic.
I have tried to stay out of this conversation, not because I don't appreciate the debate, but because I haven't completely formulated my opinion completely yet.
As TKGS pointed out above and as everyone breathing really knows unless they are in a serious state of denial, the Holy Catholic Church is in a crisis. At this point, I am reluctant to say "Clearly, there is no Pope! Jump ship!" Something about that just seems faithless to me. Perhaps that is why, currently, I find my sympathies lie with the SSPX. The organization itself is not perfect and there seem to be many problems that I am just not aware of at the time, but attending there makes sense to me.
Our priests are openly critical of some of the Popes decisions and most of his philosophy, but they aren't ready to say completely that there is no Pope.
The problems in the Church, in my humble opinion, (and I am not that smart or well read) are of a philosophical and theological nature. The problems didn't begin with the Church or even in the Church, they began with the intellectuals inside the hierarchy. For many of these intellectuals, and Ratzinger was one of them, Phenomenology was critical. In a few words, Phenomenology is the idea that it is our experiences or our understanding of those experiences that shape us and formulate our thoughts.
Phenomenology has been around forever probably but in previous times was rejected out right, maybe not identified but rejected nonetheless. But by the mid 20th century, Phenomenologists were cranking out their ideas left and right. The intellectuals in the Church were snatching these books off the bookshelves and sucking it up. They developed their ideas from men like Husserl, Heidegger, and Sartre. These ideas slowly crept into society by way of science, art, literature, philosophy, and eventually into the Church. No one stopped it because no one really could.
As I was not a Catholic until 1995, I can not say how many Popes have been influenced by Phenomenology. I haven't read many of their writings or studied much about their personal lives. It is something I need to do. But I can say that Ratzinger studied in this school of philosophy and he is highly influenced by it. Personally, I think JPII was a lunatic, uncouth, and politically motivated. I don't think viewed himself more of a civil servant than as the Vicar of Christ. He seemed to delegate Theological issues or matters of Faith to other departments.
To explain Phenomenology in a sentence or two, one might think of it this way. In my kitchen, there is a table with eight chairs. I know it's a table with eight chairs because that is what it is. A piece of wood was made into a table in chairs. For that reason, because it is a table and chairs, we sit there to eat, work, play games, etc. That is the classical view. In the view of Phenomenology there is a subtle difference. I can say it is a table and chairs because I sit there to eat, work, and play. My experience tells me that it is a table. If my experience tells me that my computer desk is my table, then that is what a table is. See?
Most people, especially modern people who are so busy, won't even recognize the difference. So in essence what happens is that God is God because we experience Him, not because He is and has always been. This is how JPII, B16 and many NO Catholics can say with confidence that "there are many paths to God, but it's all the same God."
So, yes, the Church is infiltrated from within with "modern" thinkers. Does this mean the Church doesn't exist? Of course not! Have they taken it over? Yes. But I believe the Holy Spirit is perfectly aware of this. Right now, the visible Head of the Church is also a modernist thinker. It is fitting. I cannot begin to speculate what God has in store, but I am certain, because the Deposit of Faith tells me so, that Hell will not prevail!
At this point, I can not support the sede vacante position. JPII was an obvious heretic. B16 is slicker because he pretends to be in favor of tradition but he is heavily influenced by modernist thinking. He is simply seeking to appease the trads inside the Church to prevent a true Schism. IF a Schism does happen, the everyone will be able to see the sickness in the modern Church. This is why the Pope issued MP--it's about people's experiences. In his mind, some trad minded people experience God this way and he doesn't want to isolate them. This is his thinking and he doesn't want to upset the apple cart. He just makes concessions. He is attempting to make peace within the Church.
I do believe, however, that big changes are in store and that many neo Caths make soon have to uncover their heads. I believe very soon the Pope will definitely make celibacy optional for priests. He's going to have to as many, many more Anglicans come "home" to their ordinariates. Elsewise, many "love-minded" priests will leave their Latin Rite dioceses for a short period, get married, and then petition Rome for permission to join one of the every growing Anglican Ordinariates. Solution to keep peace for Ratzinger: optional celibacy. His argument will be that this is not dogma, just tradition, and that due to changing times and an aging priesthood, celibacy is optional. It will happen. Soon. Many trad minded Catholics in the NO will freak out and won't know what to do. They really won't. Within a decade, all the priests will be married. There won't be a need for women priests right away, but that will be the next move.
I am rambling now. But that's how I see it....