Israel's turning

 Israel's future turning away from sin/ ungodliness...

I believe the references to Israel being turned away from godliness and sin is a standing and state distinction.

We read this in Romans, chapter 11:26-27, where it says "the Deliverer will come out of Zion and He will turn ungodliness from Jacob; and this is my covenant with them, when I take away their sins."

We see this also in the book of Acts where Peter talks about Israel, being blessed by the coming of Jesus, "in turning every one of you away from your iniquities," Acts 3:26.

I believe the turning away has to do with their state, their conduct, while the remission of sins has to do with their standing, their identity.

Because of the remission of sins, which changes their standing and identity before God, they will turn away from their ungodliness/ iniquities. Though not stated, remission of their sins will result in their new birth. And by the enablement of the new birth and the knowledge of the remission of their sins, they will be motivated and enabled to have a conduct consistent with their new standing with God.

We can see standing and state in Titus 2:11 that says "for the grace of God that brings salvation has appeared to all men teaching us that denying ungodliness and worldly less we should live sober, righteously, and godly in this present age, looking for the blessed hope, and glorious appearing of our great God and Savior Jesus Christ."

By the grace of God, we are saved, and that salvation teaches us to deny ungodliness and worldly lusts and to live soberly righteously and godly in this present age, as we look for the blessed Hope and glorious appearing of our great God and Savior Jesus Christ. 

The standing is not determine by the state, but the state is an expected result and a guaranteed potential of the standing—it's not automatic but is a potential reality. Because of all that will happen with Israel as a people and nation at the coming of Christ, they will be the people God wanted them to be, because of the remission of their sins, by the grace of God.