What doctrines are essential to the new birth?

The entire chapter of Hebrews 11 deals with this rather specifically. The greater half of all the people mentioned were "under the Law", including Moses himself. It mentions their works, but says it was their faith that justified them.

Did Abel's sacrifice save his soul? Hebrews says Abel performed "by faith", and therefore received the witness that he was righteous. It was saving faith that produced an outward work of obedience. Faith proved by works.

You mentioned "the law is not of faith". That is referring to putting your faith in the Law for salvation, like the Pharisees did, rather than putting your faith in God, producing an obedience to His Law. Was not the Passover part of the Law? Yet Hebrews says "By faith he kept the passover..."

I think the language of Hebrews is clear. Like the verses you cited from Psalms 106, the works committed were simply proof of the faith. Would Phineas have executed judgement, had not his faith compelled him?

 

I fully agree. "By the works of the Law shall no flesh be justified in His sight..."

I am talking about Faith as the only means of salvation. Again, Hebrews says Moses kept the passover [part of the Law] by Faith. It was Moses' faith that justified him. But his obedience to God's command proved his belief. If Moses had not kept the passover, it means he would not have been taking God seriously about what would happen with the angel of death, thus not having faith. His faith compelled his obedience. No difference than today, "Faith without works is dead".

 

Yeshua, I agree with you. Real faith produces works.

 

Habakkuk 2:4 "Behold, his soul which is lifted up is not upright in him: but the just shall live by his faith."
Quoted in Hebrews 10:24.
It's always been faith, and never works, by which God is satisfied. We are given ample examples in the OT itself.

Psalm 51
16 For thou desirest not sacrifice; else would I give it: thou delightest not in burnt offering.
17 The sacrifices of God are a broken spirit: a broken and a contrite heart, O God, thou wilt not despise.

Psalm 40:6
Sacrifice and offering thou didst not desire; mine ears hast thou opened: burnt offering and sin offering hast thou not required.

God demanded obedience to the Law in OT times. But He did not impute righteousness to the souls who observed the Law. This is very clear from Hebrews.

It has always been a humble, contrite heart of faith, which God demands.

And, "I am the LORD, I change not"