Jesus died for sins as part of a new dispensation period. The period before this required animal sacrifice of your best, most pure, as a token of seeking forgiveness but also the keeping of the law. Salvations of this type was for the Jews. That is not to say others not Jews could not be good people themselves.
When Jesus came it was to be the final sacrifice, but also at the hour of crucifixion the curtain of the temple was rented, from top to bottom, in order to show such animal sacrifices were no longer needed. Not only that but it no longer required a high priest to go into the innermost sanctum of the temple to sacrifice yearly on behalf of the Israelites. Salvation was no longer just for the Jews but for all.
In this new era, the one since then, all one needs is to accept the Spirit to dwell within in, instead of some building, and it would help us be good people. It is basically a system of salvation for all. It is a helper to not only overcome sin, because without it might be hard for us to stop sinning, but also to connect us directly to God as long as the Spirit is within.
The system allows some to be set apart, as holy, as living temples of God, to be free. Not that everyone will become perfect but it is a process of purification and getting purer so when we die we, as the Jews before, can be God's chosen people. And again that is not to say people cannot be good without it but we believe it makes it easier.
This is what we think. Without the Spirit you are none of His. You can be good on your own though and have your own clean conscience and not feel guilty. The law is still written on your heart. But those who do not have the Spirit are are not of His.
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Romans 8: 9 You, however, are not in the flesh but in the Spirit, if in fact the Spirit of God dwells in you. Anyone who does not have the Spirit of Christ does not belong to him.
Christ though did not pray for those who reject Him.
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John 17:9 I am praying for them. I am not praying for the world but for those whom you have given me, for they are yours. 10 All mine are yours, and yours are mine, and I am glorified in them
But He did pray for those who will come to believe in Him in the future, at least the future from the point of time He spoke these words. His prayer back then was for all of His people even the ones unborn who would come to Him later in their lives.
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John 17: 20 "I do not ask for these only, but also for those who will believe in me through their word, 21 that they may all be one, just as you, Father, are in me, and I in you, that they also may be in us, so that the world may believe that you have sent me.
So yes Christ died for our sins and also came to life (the more important party of the equation) so we can come to life. If one does not choose Christ then His dying for your sins is a gift you do not accept. We each have to work for out salvation ourselves and should not judge others: bottom line. So Yes, Christ died for all our sins but the gift that comes with it, the Spirit, will not be accepted by all. So in a way He died for your sins only if you let Him.