Sorry about the Latin, but I couldn't resist it. Outside the church there is no salvation? It's traditional, and most traditional Christians, when pressed, would probably quote Johannine texts like John 14:6:
Jesus said to him, "I am the way, and the truth, and the life. No one comes to the Father except through me.
The Fourth Gospel, of course, along with 1 John, is a somewhat sectarian text, and I don't doubt that the author intended this in an exclusive sense. It has been read as saying that anyone coming to God, through whatever faith, comes through Jesus whether they realise it or not. That's acontextual, but then so is most of our Bible usage. Perhaps more seriously, it patronises other faiths. However, I don't believe in approaching the Bible in a wooden, rigid way. Just because the author of the Fourth Gospel thought something, it doesn't make it true. We can't take that approach without suppressing the very real tensions and conflicts between different parts of the Biblical text, and that would be dishonest. There's also the problem that 'the church' has often become 'my church'. This is a doctrine with a history of feeding divisiveness, and that alone should start the alarm bells ringing.
The historical doctrine is intimately bound up with the concept of original sin. Doctrines didn't arise 'because the Bible says'; they formed a perfectly logical mosaic, which often owed little to the Bible. The Western church tradition held that Adam lived in a state of supernatural blessedness, from which he fell owing to pride, which led him to grasp at equality with God. He treated Satan as though he was God, fell into his power, and sin took posession of his flesh. I hardly need to point out that this idea is not to be found in Genesis! It's cobbled together from isolated texts through the Bible, many of them in Paul, and a good deal of imagination.
To get from this to original sin, we add the concept of radical human solidarity with Adam. It's worth quoting Ambrose: 'In Adam I fell, in Adam I was cast out of Paradise, in Adam I died'. Ambrosiaster, using an inaccurate translation of Romans 5:12, went further. 'It is therefore plain that all men sinned in Adam as in a lump. For Adam himself was corrupted by sin, and all whom he begat were born under sin. Thus we are all sinners from him, since we all derive from him.' Corruption is passed on through human generation, from father to son. It was believed that the woman incubated the man's seed, and contributed nothing of her own. She was thus irrelevant to the transmission of the taint. Thus the virgin birth achieves its historical importance; Jesus had no human father, and hence no original sin.
Augustine follows this tradition, and sees the baptismal liturgy, with its exorcisms and solemn renunciation of the devil as evidence of the sinfulness of infants. Baptism, to Augustine, is the sacrament which removes the guilt of original sin, without affecting its actuality; its power over our members. Thus, we continue to sin, but guilt is washed away, and the path to salvation opened to us. However, in our natural state, we have lost our liberty to do good, and without God's grace we can neither avoid evil nor do good.
It's only by baptism that the taint of original sin can be washed away, and baptism is the sacrament of initiation into the church, sometimes compared with the City of God, or the Ark adrift in the Flood. It's only by that initiation that we can hope for God's grace in salvation, hence outside the church there can be no salvation. It's logical enough, but how many modern Christians could actually agree with the above? I suggest very few!
In practice, these days we don't really believe that babies are born burdened with the guilt of Adam's sin, and we really wouldn't agree with Augustine's conclusion that a newborn baby dying unbaptised is infallibly damned. In his book, we're all heretics.
Likewise, whosoever says that those children who depart out of this life without partaking of that sacrament (Baptism) shall be made alive in Christ, certainly contradicts the apostolic declaration, and condemns the universal church, in which it is the practice to loose no time and run in haste to administer baptism to infant children, because it is believed, as an indubitable truth, that otherwise they cannot be made alive, must necessarily remain under the condemnation, of which the apostle says, " by the offence of one, judgment came upon all men to condemnation."
Letter 166.7.21, to St. Jerome.
But if we don't inherit Adam's guilt - which isn't to say that I think we can't make any sense out of original sin - then the other assumptions linked with it fall flat. We're no longer in desperate need of baptism to rescue us from damnation, and very few of us would understand it in that sort of magical sense anyway. So there seems to be no reason why God's grace should be confined to those who have been initiated into the church.
My wife is a devout Muslim; it's not a problem to us, though it sometimes is to other people. Usually, they seem to be the dogmatic type, to whom religious rules are more important than human beings. After fifteen year of daily exposure to Islam, it's only too clear that we're in agreement on vast areas of faith, and even follow similar practices at times. We pray in similar ways, with both formal and informal prayers. We worship the same God, and both understand him as a benevolent deity who makes very much the same moral demands on our behaviour. We ive in ways that aren't so very different. Obviously, there are specific areas where we differ.
Muslims believe that Jesus was a very great prophet, the bearer of the Gospel, which, along with the Law and the Psalms, is true scripture. They recognise the same prophets as we do. They tell very similar stories about the Patriarchs, with specific differences. They believe in the resurrection of the dead, and the last judgment. Their understanding of Jesus is obviously different, they don't believe in the Trinity (I wonder how many Christians have ever made a serious attempt to understand it, though!), and they believe that Jesus escaped death on the cross.
I find it impossible to believe in a good God who, when all's said and done, accepts or rejects us according to what doctrines we believe and what rituals we've undergone. I don't see that deity in the Bible either. I can see no reason to suppose that God won't accept a Christian, Muslim, Jew or whatever. If we're going to believe in a loving, compassionate God, let's be consistent about it!