1) We should never put others down or think we are holier than anyone else because God alone is our judge and we cannot judge what is in the heart of any believer. God alone can. He knows those who reject Him knowingly and unknowingly, whether in His Church or outside of it. He also sees our heart and our actions and we all have to stand in account of what we say or do... no exception... Catholic or otherwise. He knows those who honestly try to follow Him and all that He has given us and those who don't. He also knows those who have never been taught nor raised to find Him and seek Him. They will be held less accountable than the others.
2) God does bring salvation always through His Church. There is only one Baptism that all of us enter into so that we can be saved and it is Christ's Baptism and apart from Christ there is no salvation. It always come through and in Him. He handed this gift onto His Church which He set up in the beginning and upon the foundation of His Apostles to whom He said: "Upon this rock I will build My Church and the gates of the netherworld will not prevail against it. Whatsoever you bind on earth shall be bound in Heaven and whatever you loose on earth will be loosed in Heaven." So, whoever is Baptized enters into Christ's Baptism and is therefore saved and by that Baptism are a party of His Body, the Church... and yes, it is physical as well as spiritual. We can deny this left and right... but it is Christ's words and what He set up. If you have a problem, you can argue with His Word. There is also what is called a "Baptism by desire". Those who, through no fault of their own, would accept baptism if it was offered to them and who seek it and die before this can happen. And yes, the Catholic Church teaches this as well.
3) The problem lies in the fact that Christ did give us one Church and many Christians do not want to be a part of it, reject it, or do not know in their hearts that it truly is His Church. God will deal with us accordingly. If we knowingly reject what He has set up, gave us, and handed on to us and say "We don't need this", we are in trouble and accountable for that. At the same time, those who do not know this but once known would want it are saved by that desire and are therefore united to the Church by that desire.
4) The simple fact of the matter is that we all began with One Christian Church and it is called the Catholic Church. The Eastern Church spit from Rome in 1054 over the doctrine of the Holy Spirit and that rift continues to this day although there are signs of healing and I believe a very soon union again. After this the second schism was when Martin Luther cut himself off from the Catholic Church in 1517 and began the greatest division in Christianity that continues its ripples even to this day. There are now over 41,000 of them. Not all of them can be right and Jesus established one. We all were a part of Rome before Martin Luther spit away from it. Once people started to follow Martin Luther's version of Christianity, things began to change in teaching, theology, morality, etc. So, it was not Christ's version that was handed on from the split, but Martin Luther's. Hence the name "Lutheran". Once others disagreed with him or with Rome, other divisions sprang up... like the Anglican Church because Christ and His Church never allowed for divorce and the King of England wanted it (no longer following Christ's teaching handed onto us by His apostles) so he spit and thus set up his own church (No longer following what Christ handed on to us from His Apostles)... and on and on. The real question we should be asking ourselves is not whether or not I am a Christian... but whose version are we following? Christ only gave us one version and prayed that we would be one (please read the Gospel According to St. John Ch.17) and be sanctified in truth and faithfully keep His Word... not change it to our own fancy. Again, there are many Christian churches/denominations that allow for divorce... but what did Jesus day? So whose version are you following? The same it true of homosexual unions, redefining marriage, women priests, etc. What did Jesus set up vs. what are we really following? The more and more we change what was given, the further and further we pull away from Him and His Truth. We begin to live on sand, not His rock foundation.
5) Every Christian church or denomination has some truth to it and indeed seek to follow the Gospel (some have more than others... more sacraments than others, etc.) and to the degree that they have some of the truths of the Christian Faith they can be saved and are united to the Church by that Faith spiritually but not yet physically just as a husband can separate himself from his wife and not be united to her physically but is still bonded to her spiritually by marriage. However, it is much harder to be saved because each one is missing one element or another of the fullness of Truth... The fullness of the Truth divided becomes a "denomination". This is what "denomination means: a sub-group or a part of the whole. It does not mean the whole thing. For example, if you go to a bank and you ask for $1,000 they may ask you want kind of denominations would you like that i? Then proceed to give you it in parts... $100's, $50's, etc. Some of those bill will have a larger portion of the whole but it is not the complete and whole amount. Only the $1,000 bill would be the entire amount... the lesser bills would be only a portion of the whole. This is what a Christian demoniation has... a part and until we come back to the "whole" we will always be "less than the whole thing"... and the more and more we fall way, divide, change the truths that have been handed on and make our own interpretations and spit... the less and less of the whole of Christianity we will end up with which will make it harder and harder to get to Heaven. Again, this is a simple fact and simple part of Church history. Please read all of the Church history and you will see this is how we got to where we are presently at.
6) So, to the degree that other denominations have elements of the truths of salvation, they can be saved by holding onto them, which originated with the Catholic Church/early Christianity and is united to it. However, they are going to have a much harder time the more they are further away and spit from the "whole" and will have an easier time the more they are closer to and have more of the "whole". This is how "there is no salvation outside the Catholic Church" works. Again, once someone knowingly rejects Christ or what He has handed on to us, if not repented of, will not bring them salvation. Jesus even tells us this quite explicitly in the Gospels:
 Not every one that saith to me, Lord, Lord, shall enter into the kingdom of heaven: but he that doth the will of my Father who is in heaven, he shall enter into the kingdom of heaven.  Many will say to me in that day: Lord, Lord, have not we prophesied in thy name, and cast out devils in thy name, and done many miracles in thy name?  And then will I profess unto them, I never knew you: depart from me, you that work iniquity.  Every one therefore that heareth these my words, and doth them, shall be likened to a wise man that built his house upon a rock,  And the rain fell, and the floods came, and the winds blew, and they beat upon that house, and it fell not, for it was founded on a rock. And every one that heareth these my words, and doth them not, shall be like a foolish man that built his house upon the sand,  And the rain fell, and the floods came, and the winds blew, and they beat upon that house, and it fell, and great was the fall thereof. (Matthew Ch.7)
He also warns us about changing His Word which was handed on from the beginning (the King James Bible version DID change the words of Holy Scripture and took out whole and entire books of the Bible):
 For I testify to every one that heareth the words of the prophecy of this book: If any man shall add to these things, God shall add unto him the plagues written in this book.  And if any man shall take away from the words of the book of this prophecy, God shall take away his part out of the book of life, and out of the holy city, and from these things that are written in this book.  He that giveth testimony of these things, saith, Surely I come quickly: Amen. Come, Lord Jesus. (Revelations Ch.22)
Anyway, I hope this helps.
~Fr. Scott Brossart, SOLT