I know that through the death of our Lord we are made acceptable to God, but how were people in the Old Testament acceptable? There are many great figures in the Bible who made some dreadful mistakes – Jacob, Samson, David, etc. It has always been encouraging to me that God looked with favor upon these people who got things so terribly wrong; however I find it difficult to reconcile the idea that as a righteous God, they should not have been acceptable in His eyes.
I know it can’t be connected with them obeying the ‘law’ because, like the rest of us, they would never have been able to achieve it. David for instance, repented and was forgiven – how was this possible? Was it their faith that made them righteous? Was it possible for them to remain in sin and still be acceptable to God through faith?
You’ll find the answer to your question in Hebrews 10:12-14. In effect it says that although Jesus offered Himself only once on a specific day in history, His death applies across the entire span of time to all who accept it in faith, from Adam in the past to the last human to be born in the future, and makes them perfect forever in God’s sight.
Romans 4:3 says that Abraham believed God and it was credited to him as righteousness. And in Romans 4: 6-8 Paul quoted from Psalm 32:1-2 to show that David believed the same thing. The Bible makes it clear that man can only receive salvation through faith in the substitutionary death of the Messiah. It has always been that way and it will always be that way.