Luk 7:50
And He said to the woman, “Your faith has saved you; go in peace.”
I do not think you studied the issue. Did Abraham raise his knife with intent? Time and again scripture answers your question. Read all the verses that say in effect "your faith has" saved, healed, etc.
Who does Christ "know?" Those God places in Christ!!
Why does God or on what basis does God place individuals into Christ? Those whose faith God credits as righteousness.
1Th 3:6
But now that Timothy has come to us from you, and has brought us good news of
your faith and love, and that you always think kindly of us, longing to see us just as we also long to see you,
Scripture answers your question, and doctrine is not mentioned. Here is the question for you to study, what "kind" of faith does God credit as righteousness. Trust in God or trust in doctrine? Love of Christ or love of doctrine. Is "faith" referring to the information (Son of God, God incarnate, Eternal God, etc) or full blown love and devotion to Christ, no matter what?