The thing about membership in a secret society is that it cannot be PROVEN ABSOLUTELY, unless the suspected party has either been caught in the act and publicly been exposed and has no excuse or alibi, or has publicly admitted to this. These are the only ways that an excommunication could take effect in the external forum, so as to bind Catholics to the duty to reject such a one.
Membership in a secret society is just that: secret. The only way that a person could lose an ecclesiastical office in the EXTERNAL FORUM is if he was publicly known as a Mason. A secret Mason, although he would already have lost his internal union with Christ, would nevertheless be unknowable as such to "his" flock, unless he were to give himself away somehow. He would in effect be an occult heretic.
As such, "his" flock would be invincibly ignorant, as per the definition of St. Thomas Aquinas.
|St. Thomas Aquinas, Prima Secunda Partis, Q. 76, Art. 2: said:|
|Now it is evident that whoever neglects to have or do what he ought to have or do, commits a sin of omission. Wherefore through negligence, ignorance of what one is bound to know, is a sin; whereas it is not imputed as a sin to man, if he fails to know what he is unable to know. Consequently ignorance of such like things is called "invincible," because it cannot be overcome by study. For this reason such like ignorance, not being voluntary, since it is not in our power to be rid of it, is not a sin: Wherefore it is evident that no invincible ignorance is a sin. On the other hand, vincible ignorance is a sin, if it be about matters one is bound to know; but not, if it be about things one is not bound to know.|
Therefore, if he kept it secret, "his" flock would be following a heretic, they would have invincible ignorance of this fact, as such ignorance was defined by St. Thomas. So if they had already been baptized and were otherwise professing the Catholic faith whole and inviolate, then they have not lost their Catholicity, they have not committed schism, because they CANNOT KNOW that their prelate is a Mason, whereas if they could have known, they should have known and their ignorance is no longer invincible; they are culpable.
It is the difference between following a manifest heretic and an occult heretic. One you can and ought to know is heretical, the other you cannot unless he lets it slip externally.
This is where conjecture comes in. A person can guess that a man was a Mason because of his outward actions. We can even possess what is known as MORAL CERTAINTY, which is not the same thing as absolute certainty.
Moral certainty is "a very high degree of probability, sufficient for action, but short of absolute or mathematical"
Such is the case with certain papal claimants, since they are on PUBLIC RECORD as using the popular Masonic hand signal (something that just doesn't happen by accident - try it and see - to make the hand signal you have to deliberately PURPOSE to make the hand symbol). Therefore this, in addition to their very Masonic sounding words and doctrines (eugenics, birth control, New World Order) provide evidence and establish a moral certainty of their Masonic membership.
I have seen no evidence at all that Pope Pius IX was publicly known as a Mason, either at the time of his reign, or afterward.