If a window into the soul is required to say whether one is Catholic or not, then the Church isn't really a visible thing or discernible thing, is it?
In fact, it becomes hideously gnostic, and no one can be said to belong to it or be separated from it. Obama might even be Catholic. Madame Blavatsky might be playing mahjong with Voltaire in heaven. Who knows?
On the other hand, Pius XII laid out what makes a person a Catholic. Baptized and not an heretic, apostate or schismatic.
Your answer denies the distinction between material and formal heresy.
In the former, a man remains Catholic.
In the latter, he does not.
Tell me: Do you have the power to know whether a man realizes he is contradicting Church teaching, so as to pass from the material to the former?
I think you are reading these two concerns (the visibility of the Church on the one hand, and the distinction between material/formal heretic and the consequences for Church membership thereof on the other hand) in opposition to eachother.
Kind of like how a Feenyite reads the passages on water baptism as being opposed to baptism of desire.
A broader vision of the whole corpus of ecclesiology would alleviate your concerns, and bring you to the realization that the two do not oppose eachother.
Pax
I appreciate the distinction between materially holding an heresy and actually being guilty of heresy, in this case being a formal manifest heretic. Someone who materially holds a heresy submits to the teaching authority of the Church, and through ignorance believes something contrary to what She teaches. It is apparent to me that Francis neither submits to the teaching authority of the Church, and it is equally apparent that he cannot claim to know her teaching on something so basic on there being no salvation outside of her (as an example).
No one, including the Church, can judge the internal forum. She judges based on externals. She does not require a window into the soul to do so.
The Church's visibility depends in part on her members being identifiable. If, by your rule, a window into the soul is needed to know if a man is a Catholic, then the Church DOES become invisible, because no one can find a Catholic, since no one has a window into the soul-- including our Holy Mother Church.
To make the point yet another way:
Say my grandmother says "there is no Catholic God."
Tell me:
Is she Catholic (i.e., has she put herself outside the Church)?
Point B:
Does your inability to answer the question (since you cannot know the internal forum, and therefore, whether she realizes she is at odds with Catholic teaching) rob the Church of visibility?
Obviously not.
My "inability" to answer the question lies in a lack of information, not in an inherent inability to know whether or not a given person is a member of the Church. Judging the internal forum is NOT required to answer the question. If it was, the Church could NEVER declare anyone excommunicate, because even She cannot judge the internal forum. Luther, Cranmer, Zwingli, et al. could not have been condemned as they were if the Church depended on judging the internal forum.
If your grandmother knows that the Church teaches there is only one God, and a Catholic God, and denies the existence of that God or chooses to follow an idol of the gentiles, all of which are demons, then she is not a Catholic.
But there's much more than that. Francis has publicly participated in false religious services, and even submitted himself to receive a protestant "blessing" in one of them. Has your grandmother done that? This goes far, far beyond "there is no Catholic God," though that statement is bad enough.
And your argument cuts two ways. How can we know with moral certainty that Pius X was a Catholic, if his public teachings and profession of the faith do not suffice? Unless you would just assume that all the baptized are Catholics, since we cannot judge the internal forum-- in which case, what's the big deal if my Lutheran grandma receives Holy Communion at our chapel? I mean, who am I to judge, right?
But reality is much simpler and makes a whole lot more sense! Both ecclesiastical judgements (which bind the faithful) and private judgements based on moral certainty (binding to the person who forms them) are informed by externals.