Sorry that I won't have time to reply to all the various objections as I said, but this one is brief enough and several of you have mention it. In the statements such as the above quote from Lumen Gentium, the Church is not saying that Jews can be saved by/through Judaism and Muslims through Islam and Atheists through (science??), but rather, that we hold out the hope that such persons, if (IF!) they are seeking to live the truth in charity to the best of their ability and conscience, could possibly still be saved through Christ.
Now this is not an easy topic so you can't just read one paragraph of a document and then start making accusations. The Church as early as the Council of Orange in the early 5th century had already made statements about salvation only being available through Christ, and these have been reaffirmed in various councils, particularly Trent in answer to the Reformers. So the idea is not that there are other saviors besides Christ, but rather that because God IS Truth and IS Charity, we Hope (note well, we hope, not that it is certain but that we have to at least hope and pray), that those who have had no chance to know Christ could still be saved by Him because they have sought Him in seeking the Truth and Charity. So think for instance of the Last Judgement in Matthew, those who are saved are those who feed the poor and visited the imprisoned etc, and those who are condemned say "but Lord didn't we...". Now don't confuse me for trying to teach salvation by works which I already can hear people jumping into, but the Church merely recognizes that while we know that Christ alone is the savior it seems like a good idea to hope and pray for the millions and millions of people who will never have the chance to know Him by name, and believe that because He is a good Savior it might be possible for Him to finds means to save such persons.
To deny this hope is to admit that there are millions of people who God created without giving any chance of salvation. Think of the people living on other continents 5 minutes after Jesus died. They would have no chance to ever hear of this beautiful story about the God who entered into His creation to rescue His lost bride. So the Church atleast says we can't condemn them and we hope that God can save them throught he little knowledge of His Son that they would have from their conscience and reason which are glimmers of the image of God in man which He implanted that we might know Him.
As CS Lewis (an Anglican

) says: "I
s it not frightfully unfair that this new life should beconfined to people who have heard of Christ and been able to believe in Him? But the truth is God hasnot told us what His arrangements about the other people are. We do know that no man can be savedexcept through Christ; we do not know that only those who know Him can be saved through Him"
I don't expect that to be an exhaustive explanation of the matter to convince you, but it is just to go to show you that you have to be able to understand something of the context of these teachings to understand them correctly.