Q. I heard Catholics think their Church is the only true one and you have to belong to it to go to heaven. Is that true?
A. Yes, no, and maybe so. Catholics believe it is not out of the realm of God's mercy to save non-Catholics. However he has given us sure the way to do it, which is the Catholic Church and the Sacraments. During my catechism classes before Confirmation my priest explained it to me like this:
Suppose you are on the roof of a burning building. Your options are limited. You can either jump off the top or take the fire proof stairwell safely to the bottom. Survival is possible for those who jump, but survival is guaranteed for those who take the stairs. In this analogy, the fire proof stairwell is the Catholic Church.
A couple more points you should be familiar with. The Church in the past has taught that there is "no salvation outside the Catholic Church." (Unam Sanctam, PP. Boniface VIII) It absolutely still holds this view. However for those who are not aware of the Christ or the Church's teaching they cannot be held responsible and sent to Hell. For their part, they are responsible for living a moral life to the best of their knowledge and will. We on their behalf pray and hope for God's mercy. Non-Catholic Christians may or may not fit this mold. However if they are saved (and on a personal note, I believe many are) it is in some way through the Catholic Church, even though they may not physically belong to her. You can read more about that in Gaudium et spes, linked below.
When I was growing up in the Presbyterian Church U.S.A my Sunday School teachers taught us that people who never hear about Jesus Christ go to hell so that is why we have missionaries. I continued to hold this view even through my college years though I never gave it much thought (or worry). I don't think all of the PC-USA holds this, but its something that sticks out in my memory.
Important: Catholics recognize all Trinitarian baptized people as brothers and sisters in Christ. They are Christians, and need to be afforded Christian charity. Unfortunately, this does exclude groups such as the Mormons. We believe that from the moment someone is baptized, they are Catholic until a conscious decision is made by them to the contrary. This is believed because the sacrament of baptism is not dependent on who gives it or who receives it, only its form and intent.
The standard trinitarian baptism found everywhere is: "I baptize you in the name of the Father, Son, and Holy Spirit." That is what makes you a Christian and a Catholic. If you are baptized as an adult, we believe in addition to washing away your original sin (more on that later) it removes any and all sins you have committed up to that point. In a later post on Sacraments I will explain how and why we believe that.
Q. What is the point of Ecumenism?
A. Ecumenism is kind of the new kid on the block for Christians. Before the 20th Century all the different kinds of Christians didn't get along so well. In some cases they still don't. But the Catholic Church since the 1960s has been working hard to communicate with our separated brethren. This is particularly true with the Orthodox faithful, with whom our faith is nearly identical.
The point of Ecumenism is to fix our differences and unify - visibly. It is not to sit back and be satisfied with our huge gaping differences. It is viewed as a horrible scandal that those who follow Christ argue over his most important messages. Therefore we work to dissolve these differences in the spirit of humility and devotion. As Christ said, "so that the world may know them."
References for further understanding:
Gaudium et spes (On the Church and the Modern World), Second Vatican Council
Mystici Corporis Christi (The Mystical Body of Christ), Pius XII
Mystici Corporis Christi, in my opinion is one of the most amazing Christological writings I have ever read.
I hope you got something out of this first post. I am not a theologian, so I can only do my best. If anyone has any suggestions or corrections, feel free to let me know. One thing we're not going to do is get into an apologetics battle.
Next in the series:
Catholic Ecclesiology: Formation, the Pope, the Bishops, and all that.