In her later years my Mother moved from the independent Bible Church in which we grew up to join a Presbyterian Church. At the Presbyterian Church they recited the Apostles’ Creed each week, so on one of my visits home I asked Mom what she meant when she said she believed in One, Holy, Catholic and Apostolic Church. Especially what did she understand “Catholic” to mean.

She answered correctly, that “Catholic” means “universal” and she understood this to mean “all those who have truly given their heart to the Lord Jesus in faith–and are known to him alone.” She was articulating something that was expressed a bit differently by a sweet older Baptist lady who attended Mass with her Catholic husband. At the church door she would regularly grasp my hand, and with a warm smile and a cheerful confidence declare that she was “a Baptist Catholic.”

What my mother and the Baptist lady were expressing is something Catholics also believe. It is a belief in the “invisible Church” The invisible church consists, like my mom said, “Of all true Christians”. Catholics believe that church subsists in the Catholic Church.

The Catechism of the Catholic Church explains it this way:

“Fully incorporated into the society of the Church are those who, possessing the Spirit of Christ, accept all the means of salvation given to the Church together with her entire organization, and who — by the bonds constituted by the profession of faith, the sacraments, ecclesiastical government, and communion — are joined in the visible structure of the Church of Christ, who rules her through the Supreme Pontiff and the bishops. Even though incorporated into the Church, one who does not however persevere in charity is not saved. He remains indeed in the bosom of the Church, but ‘in body’ not ‘in heart.'”
“The Church knows that she is joined in many ways to the baptized who are honored by the name of Christian, but do not profess the Catholic faith in its entirety or have not preserved unity or communion under the successor of Peter.” Those “who believe in Christ and have been properly baptized are put in a certain, although imperfect, communion with the Catholic Church.” With the Orthodox Churches, this communion is so profound “that it lacks little to attain the fullness that would permit a common celebration of the Lord’s Eucharist.”
To put it another way, “The Church of Jesus Christ is varied and diverse and often difficult to define. However, if you want to be sure of not just the invisible, but also the visible church, then that would be the one that was not only founded by Jesus Christ himself on the leadership and profession of faith of Peter the Apostle, but also the one which today is visible universal–established in every place in the world in a visible, sacramental, juridical and real way…and that would be the Catholic Church.
I realize that many Christians may well recognize this visible universality of the Catholic Church, but resist coming into full communion with her. There are many reasons for this–some good and some not so good. Perhaps the non-Catholic Christian honestly cannot get their head (and heart) around particular Catholic doctrines and devotions. In my experience this is very often based in a sincere misunderstanding of these doctrines and devotions. Much of my apologetics writing in the past has been an effort to clarify these matters.  (see my books More Christianity and An Answer Not an Argument.) The corruption and heterodoxy of Catholic clergy and members of the hierarchy keeps many sincere Christians from taking the step to enter the Catholic Church. If and when they do attend a Catholic Mass many non-Catholic Christians are put off by the externals. Either the worship is very “high” with ornate ceremonial, extensive use of Latin and inaccessible music or they have come to the Catholic Church actually wanting that sort of thing and instead they find brutal architecture, banal preaching, bad pop music and an experience awash in sentimentality, bland do-goodism and politically correct hogwash. No wonder a friend of mine in England entitled her book encouraging converts, Come on In Its Awful! 
While these objections are understandable, I think the majority of non-Catholic Christians–like my Mom and the Baptist lady–would simply not understand or think there is any reason for them to become Catholic. They’re good. They love Jesus. They’re saved and going to heaven. Furthermore, they accept all the other people who also say they’re Christians. Why this need to be exclusive? Why is there any need to become Catholic? They are already Catholic. They belong to the invisible Church. Isn’t that good enough?
This idea that what they have is “already Catholic” was expressed in a different way by the Anglicans. When I was in the Church of England the Anglicans–and especially the Anglo-Catholics–would protest, “But we’re already Catholic. Just not Roman Catholic.” The Anglo-Catholics certainly looked Catholic and some of them liked to say, “We’re more Catholic than the Catholics!” meaning they enjoyed a more ornate ceremonial, had nicer vestments, more beautiful buildings, successful pilgrimages to Walsingham, longer tassels, bigger phylacteries etc. etc. etc. With all the externals in place–and an extravagant legend about how Christianity first came to Celtic Britain from Coptic Egypt (and was therefore distinct from Rome) it was easy to buy into the “we’re Catholic already” claim.
But isn’t that good enough?
No it isn’t, and here’s why: The Church is the Body of Christ and Christ had a real human body. The Son of God took flesh of the Blessed Virgin Mary and dwelt on this earth for thirty three years, locked into human history at a particular place in a particular time participating in particular political and historical circumstances. He was not an invisible Spirit floating around in that time period and in that place. He was a real man with real flesh and blood. After his death his body really did rise from the dead. It was not a “spiritual” resurrection. We do not say with the modernists, “In some wonderful way the sublime  teachings of Jesus continued after his tragic death.” No. We say he rose from the dead in a particular garden outside a particular city on a particular Spring morning.
In other words, because we believe in the Incarnation of Our Lord Jesus Christ we also believe in the physical, real, objective, visible Body of Christ–the Church. The Catholic Church does not just believe in the “real presence” she is the real presence–the sacrament of salvation in the world. The Catholic Church, despite all her human frailties, faults and foibles, is in a literal way The Body of Christ. She does today in the world what he did when he was here: to teach the truth, to heal the sick, to forgive sins and to take authority over evil.
To extend this in the other direction, to believe that Christ was not fully human–that he only seemed to be human or that Christ only inspired the human Jesus–or in some other way Christ remained invisible and not fully incarnate–is to lapse into a Gnostic heresy. We see this in contemporary Christianity in modern Biblical scholarship which dissects the gospel to deny the hisoricity and replace the historical Jesus with the “Christ of faith”–in other words, a legendary religious teacher whose teachings one admires.
We also see it with the extreme subjectivism that dominates modern Christianity. This is expressed in various ways: “All that really matters is how much you love Jesus” or “What really matters is the Christ spirit within you” or “I believe Jesus is present everywhere and all I need to do is find him and love him wherever he appears” or “The Christ is the striving of each human soul toward goodness” or “I’m closer to Jesus on a hike in the woods than going to church on Sunday” or…you can come up with many more such sentimental subjective notions. All of them reject a visible church.
In each case, what is resisted is the idea that there is any objective, historically verifiable, rational, Biblically based, physical and identifiable spiritual authority to which one owes allegiance and filial affection.
“No.” They will insist:  “The invisible church is good enough.”
Are non-Catholic Christians true Christians? Yes–many follow the Lord more faithfully than many Catholics. Do ministers who work within the invisible church also minister Christ’s saving work in the world?  Yes, but in a partial way–likewise unworthy Catholics live in Christ and administer Christ’s saving work in a partial way. All of us need to move further up and further in to the fullness of the Lord Jesus Christ in the world.
The Catholic faith is always both/and. So we affirm with my mom and the Baptist lady the reality of the invisible church and our shared Christian faith with non-Catholics, but we also affirm the fullness of Christ’s visible church manifested in the Catholic Church centered in Rome and built on the foundation of the preaching and the persons of Saint Peter and Saint Paul.