Don’t Catholics believe we’re in that same Church anyways? Just in some sort of broken way?
Regardless, we believe we’re all in that Church.
James covering the CCC answered this question excellently.
So would you say that some Protestants are members of the Church? Or no Protestants are members of the Church?
Let’s not look at belonging and communion as membership. After all, it is not a club

.
Let’s look at it at how the Church communion has operated throughout history (In a very compressed manner).
- What is normally the first step to enter into the Church and the Christian life? Baptism.
- How many Christian baptisms there are? One.
- How many Christian faiths there are? One.
- How many bodies (Church) of Christ there are? One.
- How many Christian communions there are? Many.
- What is this lack of communion doing? Breaking/Separating the body (Church) of Christ.
Why is communion so important for the body of Christ? Because it is the pinnacle of the Christian life on earth.
Acts 2:42 And they devoted themselves to the apostles’ teaching and fellowship, to the breaking of bread and the prayers. 43 And fear came upon every soul; and many wonders and signs were done through the apostles. 44 And all who believed were together and had all things in common; 45 and they sold their possessions and goods and distributed them to all, as any had need. 46 And day by day, attending the temple together and breaking bread in their homes, they partook of food with glad and generous hearts, 47 praising God and having favor with all the people. And the Lord added to their number day by day those who were being saved.
In the breaking of the bread (communion–Eucharist–) we affirm together one faith, a common belief and a common life in Christ.
Baptism doesn’t guarantee being in communion with the Church. If your actions are the fruit of sin (dissension for example) and not of the spirit you are then negating the graces given to you from baptism.
Galatians 5:16 But I say, walk by the Spirit, and do not gratify the desires of the flesh. 17 For the desires of the flesh are against the Spirit, and the desires of the Spirit are against the flesh; for these are opposed to each other, to prevent you from doing what you would. 18 But if you are led by the Spirit you are not under the law. 19 Now the works of the flesh are plain: immorality, impurity, licentiousness, 20 idolatry, sorcery, enmity, strife, jealousy, anger, selfishness, dissension, party spirit, 21 envy,[a] drunkenness, carousing, and the like. I warn you, as I warned you before, that those who do such things shall not inherit the kingdom of God. 22 But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness, self-control; against such there is no law. 24 And those who belong to Christ Jesus have crucified the flesh with its passions and desires. 25 If we live by the Spirit, let us also walk by the Spirit. 26 Let us have no self-conceit, no provoking of one another, no envy of one another.
If in your actions, the works of the flesh are manifest and you purposefully work against the Church, your actions separate you from the Church (See some of the heretics like Arius, Nestorius who were in communion of the Church). In the same manner, if you come to the knowledge of the truth about the Church and ignore it or deny it - you are placing yourself outside the Church in knowledge of such action. Therefore invisible ignorance does not apply.
So instead of membership, see it as communion.
Even Justin Martyr (2nd century) is clear on communion:
And this food is called among us Eukaristia [the **Eucharist
], **of which no one is allowed to partake but the man who believes that the things which we teach are true, and who has been washed with the washing that is for the remission of sins, and unto regeneration, and who is so living as Christ has enjoined. **For not as common bread and common drink do we receive these; but in like manner as Jesus Christ our Saviour, having been made flesh by the Word of God, had both flesh and blood for our salvation, so likewise have we been taught that the food which is blessed by the prayer of His word, and from which our blood and flesh by transmutation are nourished, is the flesh and blood of that Jesus who was made flesh.
Since there is one baptism and this one baptism has been handed down as a Sacrament and Command from Christ to His Apostles/Church and the Apostles have taught this one baptism to their disciples in the One Church - there can only be one Christian baptism - which unites us people into the washing for the remission of sins and unto regeneration into a life of Christ.
So the “invincibly ignorant” are a part of the Church or not?
From Dominus Iesus:
On the other hand, the ecclesial communities which have not preserved the valid Episcopate and the genuine and integral substance of the Eucharistic mystery,61 are not Churches in the proper sense; however, those (People) who are baptized in these communities are, by Baptism, incorporated in Christ and thus are in a certain communion, albeit imperfect, with the Church.
(Emphasis mine)
Again, I’d stay away from using membership - after all there is no membership card to carry that I know of
