Look I am a no nothing schmoe, and I'll probably type this poorly, but I'll give it a shot. This is how I read it...
Christ is God's love made flesh. An act of God to show his love of us by paying our debt of sin.
John 14:6 I am the way and the truth and the life. No one comes to the Father except through me.
Means no one will come to God but through His love.
Matthew 7 21“Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven. 22On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?’ 23And then will I declare to them, ‘I never knew you; depart from me, you workers of lawlessness.’
I would think this applies to doing the Jewish sacrifices. Just doing things by rote without doing the will of the Father isn't going to get you to Heaven. Much like Cain's sacrifice without Faith was rejected.
John 14 21 Whoever has my commands and keeps them is the one who loves me. The one who loves me will be loved by my Father, and I too will love them and show myself to them.”22 Then Judas (not Judas Iscariot) said, “But, Lord, why do you intend to show yourself to us and not to the world?” 23 Jesus replied, “Anyone who loves me will obey my teaching. My Father will love them, and we will come to them and make our home with them. 24 Anyone who does not love me will not obey my teaching. These words you hear are not my own; they belong to the Father who sent me.
Thus I also believe if you never heard of Christ's existence, you could, theoretically, be saved. A man 1000 years before Christ on an island alone can realize his inevitable death and say "I am weak and flawed. I am wholly at the power of the One who made it all. Only by Him may I be saved and thus I will do all I can which is right by Him. Yet because I am flawed I know I cannot earn this perfect mercy so it must be by love that you give it. Thus if you love me with my flaws you must love others and so I too love them desiring to do your will." Also known as Matthew 22 34-40 the commandments for which all the law hangs. Unfortunately every culture I know of did not do this they instead made gods in their own image which were just as flawed as they. Now just to be explicitly clear I'll preempt questions...
Gasp, are you actually saying you can be saved without Christ!
NO. I am saying it is Christ knowing us, and he knows us by doing his will, that matters for our salvation not us knowing his Earthly "name" and history. He would know us if we kept his commandments regardless of where we got them. Yet had Christ known us we would have accepted Christ having been told of Him because God is in Christ and we were already pursuing God's will. There are plenty of "Christians" who know his name and do not do his will. If you doubt ask this do you believe unborn children can enter heaven? The important point here is it is God's judgement over them that matters not that they never knew Christ by "name".
Then what's the point of telling people about Christ?
The point is we cannot know people's hearts nor know if they do God's will. Thus the Holy Spirit can work through us for their salvation and acceptance of Christ.
Bringing this back to the Jewish sacrifices it is again theoretically possible, though extremely unlikely, someone doing them could be like that man on an island who, having never heard of Christ, could be saved. Though if they were and heard who Christ was they would know and accept him. It is the rejection of Christ, and thus the Holy Spirit, which condemns them not the Jewish sacrifices.
...and yes I know Christ's sacrifice paid a debt too but a debt is paid whether we have knowledge of the act or not. It is our choice to accept or reject that payment that matters.