It is a myth that Christians think they are good people, entitled to sit in judgment over others because they are morally superior. On the contrary, a true Christian knows with certainty they are NOT good, that they are no better than anyone else... that they are rebel sinners who justly deserve God's wrath ... and that's why they need a merciful Savior who, in spite of themselves, forgives them, adopts them as His children and gives them a seat at His table.
So if a Christian points out that you need a Savior, it isn't because he hates you, or thinks he is better. No, it's because he loves you and is just like you. He shares a common humanity with you and is a sinner like you and wants you to know God's love and forgiveness in Christ.
We are better than the world we are children if God, we are a royal Priesthood we can come boldly to his throne, we have been made righteous we have been cleanse we have been given a new heart a new nature, we have been given the Holy Spirit, we are now called saints, we are set apart for a great purpose, we now know the mind of God through Christ because he reveled himself through him, a son is better than a slave, not because we chose him but because he chose us. God has called us to be a light and guide for them to our father, and invite them to know Him fear him, to honor Him, Respect Him. We fall short of his glory yes but we have been given a real hope we are Harold’s of the the good news. Christian never deny the titles and the blessings And the identities that Christ has given his children, never be ashamed of being adopted by your father.
You said "we are better than the world" So does this mean you tell your unbelieving friends that you are saved because you are better than they are? That you deserve heaven more than they do? That God favors you because you are more moral than they are? If you answered "no" to these questions it is because you understand that everything you have is because of God's mercy. Anything good you have you ascribe to Christ, not yourself. You did not earn any of it. It was given to you. You are not saved because you are better. And every day you rely upon grace for what you have.
Unless we come to the lost with this perspective they will view you as arrogant and, as such, you get in the way of the gospel, which is offensive enough on it's own. No need to add offense. Yes praise the Lord we are saints, yes we are declared righteous, but as explained in the OP that is because God forgave us in Christ. It is ONLY because God is gracious. Always point to Him, not to yourself. When you do say anything of self then ascribe glory to Christ and His grace instead of declaring that you are better than they are.
I think what sets us apart is our humility and servitude. We are no longer living among the prideful and arrogant. We are willing to repent and walk away from the sins that once held us captive, have become a new creation. We seek purity/holiness, as opposed to the wickedness that surrounds us. We are despised and rejected because we thrive for peace, tranquility...life, as it is meant to be.
Everything good you have is by the grace of God. As Augustine said, "to will is of nature, to will aright us of grace". Given what you have said, do you tell this to your unbelieving friends, that what sets me apart from you is that I am humble and you're not? Do you say, I am not prideful like you? I am better because I am willing to repent. To do so would be to ascribe your repenting and believing to your own wisdom, sound judgment or good sense and not to Christ alone. The ONLY reason you are not held captive by sin is because of mercy. Your willingness, faith repentance are themselves the gift of God. God not only saved you, He sustains you. Every breath. Every desire to persevere is a gift. Give glory to God.
I don’t tell my friends that what I have is because I deserve it but rather because he’s mercy and grace of granting those he chose the gift of repentance, the gift to be born again the gift of faith to trust him the miracle of regeneration, the granting of making us alive, opening my eyes to the Beauty of His Son the gospel, his plan to save men and how he redeems them. But I don’t go around saying I am as bad and wicked as they are, because then they would say then why come to Christ if you are as bad and wicked sinner as I am. Rather I share the Gospel to them and call them to repent of there sins, and to cry out to God for mercy for it does not depend on man but of whom God grants his mercy. We as Christians should hold fast to the identity that Christ has given us, the great privilege that we now have, never be ashamed of who we are in Christ. We may do have remaining corruption but that is not our identity for we are in Christ, That why Pail is not ashamed to begin his letters to the churches as Saints.
You said, "I don’t tell my friends that what I have is because I deserve it but rather because he’s mercy and grace of granting those he chose the gift of repentance,"
So, in the end, you do in fact tell them you don't deserve it and that you need mercy. You need mercy because you DESERVE God's wrath. right? That is exactly what I am saying. However, you don't seem to get that repentance is not just something that happened one time when you prayed a prayer in the past... Christ intercedes for you daily, NOW because you sin. You are not a sinless creature, even after redemption. So if you really understand the reality of sin in your life you will be repenting every day. You may have different sins than you did before but you need to pray daily for the grace to obey His commands. And why do you need to pray every day? Because left to yourself you would fail miserably, as would I. You are not only saved initially by grace but you are sustained by grace.
I believe, one of the greatest barriers to evangelism is Christians (or moralists) who think they are saved because they are better then their neighbor. This is exactly the reason so many non-believers perceive that Christians look down on them and judge them because Christians typically do not come to their neighbors fist taking the log out of their own eye in order to take the speck out of theirs. That means humility and recognizing that you are a beggar leading other beggars to bread. If the Lord has changed your character then that should speak for itself. You don't need to say anything.
So I believe it is quite wrong for us to claim we no longer identify as sinners. We are both righteous and sinners at the same time and we should not hide that fact. Our main identity, as I said in the OP is that God has forgiven us, adopted us as His children and given us a seat at His table. But we are to daily be putting to death the old nature because the flesh and sin still exists.