Yes, per Scripture, Christ Himself, and at least 3 dogmatic, infallible decrees.
.There are differences between the 2, but both contradict Scripture, Christ and the 3 dogmatic decrees.  Pius IX's theories are orthodox only if understood in the ENTIRE context of his encyclical, and only if understood in the context of Scripture and doctrine.  This applies to ALL papal docuмents, for all popes, for all times.
.So what?  Just because a pope writes or speaks about something, doesn't mean it's dogma.  Just because he used the phrase "I.I." doesn't mean he meant it in the same way as you or anyone in our modernist times are using it.  I guarantee you that this term is used by V2 supporters differently than you and differently than Pius IX meant it.  Context matters.
.If you aren't reading encylicals and councils through the lens of defined, infallible doctrine, then you are attempting to 'privately interpret' in the same way as do protestants.  What do you think he meant when he said that an ignorant person could be "enlighted with divine grace" before they die?  If that doesn't mean they will join the Church, then what does it mean?
.
Again, if a person can die in invincible ignorance and gain heaven, then why do they need to be "enlightened with Divine grace"?  What's the point?Fixed the above sentence for you.  If you believe that an ignorant person can gain heaven, while still being ignorant, you are a heretic.  That's not Catholic teaching and it denies Scripture and multiple doctrines.

When one describes the typical souls who are in Limbo, having died without mortal sin, but unbaptized, the normal examples are young children and the mentally handicapped.  However, these requirements could also be applied to adults...especially if invincible ignorance exists.  (Personally I don’t believe in invincible ignorance), but why can’t an adult be in Limbo?  What’s the difference between Limbo and the least-worst part of hell for those adults who only died with original sin?  

Though Limbo is a part of Hell, it only contains children who died unbaptized before the age of reason, there are no adults. Limbo is different in that the children suffer absolutely no pains like those in Hell.  The adults in Hell suffer the pains of Hell to different degrees according to God's justice.  The children in Limbo also do not really suffer the loss of God because they never knew it.

Is an Orthodox infant who is baptized a “member” of the Catholic Church?
Or is he, being in the state of grace, simply “joined to” the Church?
I contend the latter

When one describes the typical souls who are in Limbo, having died without mortal sin, but unbaptized, the normal examples are young children and the mentally handicapped.  However, these requirements could also be applied to adults...especially if invincible ignorance exists.  (Personally I don’t believe in invincible ignorance), but why can’t an adult be in Limbo?  What’s the difference between Limbo and the least-worst part of hell for those adults who only died with original sin?  

Though Limbo is a part of Hell, it only contains children (and mentally handicapped) who died unbaptized before the age of reason, there are no adults. Limbo is different in that the children suffer absolutely no pains like those in Hell.  The adults in Hell suffer the pains of Hell to different degrees according to God's justice.  That is the difference. The children live in an earthly paradise. The children in Limbo also do not really suffer the loss of God because they never knew of His existence, so they can't know what they are missing.

Pax Vobis also asked: However, these requirements could also be applied to adults...especially if invincible ignorance exists.  (Personally I don’t believe in invincible ignorance), but why can’t an adult be in Limbo?

He who is of God hears the words of God. Therefore, you hear them not, because you are not of God. St. John 8:47


That whatever is done through ignorance must not be considered a sin, is hereby condemned as error. Pope Innocent II

 
It does not suffice to say: "If I had known that such a thing were forbidden by the law of God, I would have conformed." St. Paul, in persecuting Christians, previous to his conversion, did not think that he was committing evil; the same may be said of Jews who persecuted and crucified Christ. And yet, Saint Paul and these Jews were not innocent and excusable. If they had died in that state, they would never have been saved. Hence, St. Paul, despite the good faith he acted on, acknowledges that he was at that time a blasphemer, and unjust: a persecutor of the Church. If, therefore, a person be ignorant of what is commanded­ or forbidden because he has not studied the law of God, his ignorance does not excuse him from sin.  St. Alphonsus Maria Liguori

 
If ignorance is not a sin, then Saul did not sin when he persecuted the Church, because he surely did this in ignorance. Therefore, he should not have said: “I obtained the mercy of God” (I Tim 1:13), but rather “I received my reward”.  St. Bernard

 
It may be true that there are, in the remotest parts of the world, some people who have not yet seen the light of the Savior. Certainly, God's manifold and ineffable goodness has always provided, and still provides, for all mankind in such a way that not one of the reprobates can find an excuse as though he had been refused the light of truth.

 
But if Christ "enlightens every man who comes into this world" (Jn. 1:9) 1:9) why have so many remained unenlightened? How then does Christ "enlighten every man"? He does so, as far as in Him lies. For grace is poured out over everyone. It is easily attainable by  (St. Prosper of Aquitaine)

 
The Gentiles walk in vanity, having their understanding darkened, being alienated from the life of God through the ignorance in them because of the blindness of their hearts. Ephesians 4:17-18

 
For their own malice blinded them. Wisdom 2:21

 
Those who keep their eyes shut cannot see. God made you without your knowledge, but He does not justify you without your willing it. Refusal to hear the truth leads to sin, and that sin itself is punishment for the preceding sin. Every sinner is inexcusable whether he knows it or not. For ignorance itself, in those who do not want to know, is without doubt a sin; and, in those unable to know, is the penalty of sin. In neither case, then, is there a just excuse, but in both cases there is a just condemnation.  St. Augustine

 
It follows that ignorance has the nature of mortal sin on account of either a preceding negligence, or the consequent result; and, for this reason, ignorance is reckoned one of the general causes of sin. All sin proceeds from ignorance. St. Thomas Aquinas

 
I will destroy men off the face of the earth, saith the Lord: those who turn away from following after the Lord, and those who have not sought after the Lord nor searched after Him.  Sophonias 1:3,6

 
Those who perish do not receive the love of truth in order that they might be saved. Therefore, God will send them the operation of error, to believe lying, so that all may be judged who have not believed the truth but have consented to iniquity. II Thessalonians 2:10‑11

 
No one is lost without knowing it, and no one is deceived without wanting to be. St Teresa of Avila

 
But why is it that so many men are ignorant, even at this day? This is the reason: "The light has come into the world, but men loved darkness rather than the light" (Jn. 3:19). They have not known Him, and do not know Him, because they do not want to know Him, loving instead the darkness of sin rather than the light of grace.  St. Alphonsus Maria Liguori

 
Unbelief has the character of guilt from resisting the faith, rather than from mere absence of the faith. St Thomas Aquinas

 
Innumerable souls are miserably lost through ignorance of religion the source of every other calamity. St Frances Xavier Cabrini

 
If you are ignorant of the truths of the faith, You are obliged to learn them. Every Christian is bound to learn the Creed, the Our Father, or the Hail Mary under pain of mortal sin. Many have no idea of the Most Holy Trinity, the Incarnation, mortal sin, judgment, Paradise, Hell, or Eternity; and this deplorable ignorance damns them.   St Alphonsus Maria Liguori

 
Reflect on the ruin of souls wrought by this single cause: ignorance of truths which must be known by all men alike in order that they may attain eternal salvation. This we solemnly affirm: the majority of those condemned to eternal Punishment fall into everlasting misfortune through ignorance of the Mysteries of the faith, which must necessarily be known and believed by all who belong to the Elect. Pope St. Pius X


My heart is penetrated with grief when I think of the almost infinite number of souls who are damned for lack of knowing the true God and the Christian reli­gion. The greatest misfortune, O my God, is not to know Thee, and the greatest punishment not to love Thee.  St. Louis Marie de Montfort

 
Before their Baptism, certain Japanese were greatly troubled by a hateful scruple: that God did not appear merciful, because He had never made Himself known to the Japanese people before, especially that those who had not worshipped God were doomed to everlasting Hell. They grieve over the fate of their departed children, parents, and relatives; so they ask if there is any way to free them by prayer from the eternal misery. And I am obliged to answer: there is absolutely none. St. Francis Xavier

 

The excuse of ignorance is denied those who know the commandments of God, but neither will those who do not know be without punishment. "For, as many as have sinned outside the law shall also perish outside the law" (Romans 2:12). Without faith in Christ, no man can be delivered; therefore, they will be judged in such a way that they perish. "The ser­vant who does not know his Lord's will, and who commits things worthy of stripes, shall be beaten with few stripes‑, whereas, the servant who knows his Lord's will, shall be beaten with many stripes" (Lk. 12:47‑48). Observe here that it is a more ser­ious matter for a man to sin with knowledge than in ignorance. And yet, we must not take refuge on this account to shades of ignorance, to find our excuse therein. Even ignorance which belongs to them who are, as‑it‑were, simply ignorant does not excuse any­ one so as to exempt him from eternal fire, even were his failure to believe the result of not having heard at all what he should believe. It was not said with­ out reason: "Pour out Thy wrath upon the nations who have not known Thee" (Psalm 78:6), and "He shall come from Heaven in a flame of fire to take vengeance on those who do not know God" (Thess.11 1:7‑8)  St. Augustine

 
The crime of ignoring the Lord is not less than that of offending Him. Ignorance of God is sufficient reason for punishment  Minucius Felix

 
And if our Gospel be hidden, it is hidden from those who are perishing, in whom the god of this world has blinded the minds of unbelievers, in order that the light of the Gospel should not shine unto them. II Corinthians 4:3‑4


An ignorant person is like a dying man lying unconscious: he does not know either the malice of sin or the value of his soul. He goes from sin to sin, like a rag dragged through the mire.St. John Mary Vianney

Perhaps he who asserts that a person cannot sin through ignorance never prays for his ignorances, but laughs at the prophet who prays: "O Lord, re­member not the sins of my ignorances!" (Ps. 24:7). Perhaps he even reproves God, Who requires satisfaction for the sin of ignorance, for in Leviticus He speaks of "sin through ignorance." If ignorance were never a sin, why is it that the High Priest entered the second tabernacle with blood, which he offered "for his own ignorance and for the ignorance of the people" (Heb. 9:7)? If one never sins through ignorance, then what do we hold against those who killed the Apostles, since they truly did not know that to kill them was evil but rather thought that they were "doing a service to God" (Jn. 16:2). Thus, also, Our Sa­vior prayed in vain on the cross for those who cruci­fied Him since, as He Himself testifies, they were ig­norant of what they were doing (Lk. 23:34) and thus they did not sin at all! Neither should anyone suspect that the Apostle could have lied when he said: "For, if they had known it, they would never have crucified the Lord" (I Corinth. 2:8). Is it not sufficiently clear, from these passages, in what great ignorance the man lies who does not know that one can some­ times sin through ignorance?  St. Bernard