Yes, He did save us and gave us eternal life, too. If we don't hate sin, the Lord hasn't circumcised our hearts, we've only tried to circumcise our own. In other words, we haven't been born again a new creation. We can't go by what man professes...only the Lord knows the heart of man. When believers sin, they put themselves out of fellowhip with the Lord, but He is faithful where we are not, and He will lose none the Father has given Him.
The Gentiles, the whole world, have been brought into the New Covenant...we get saved by grace through faith when we believe. Mankind has been reconciled to God through the cross and the blood, we still need to be born again in order to obtain the promises. In Romans 11, Paul is not talking about being "grafted" into Christ. We must be born into newness of life.
When you are born into newness of life, you are also grafted into christ and grafted into Israel; i.e. you become a jew!
Rom 2:25-29
For circumcision is indeed profitable if you keep the law; but if you are a breaker of the law, your circumcision has become uncircumcision. 26 Therefore, if an uncircumcised man keeps the righteous requirements of the law, will not his uncircumcision be counted as circumcision? 27 And will not the physically uncircumcised, if he fulfills the law, judge you who, even with your written code and circumcision, are a transgressor of the law? 28 For he is not a Jew who is one outwardly, nor is circumcision that which is outward in the flesh; 29 but he is a Jew who is one inwardly; and circumcision is that of the heart, in the Spirit, not in the letter; whose praise is not from men but from God. NKJV
Rom 11:15-26
15 For if the casting away of them be the reconciling of the world, what shall the receiving of them be, but life from the dead?
16 For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches.
17 And if some of the branches be broken off, and thou, being a wild olive tree, wert graffed in among them, and with them partakest of the root and fatness of the olive tree;
18 Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee.
19 Thou wilt say then, The branches were broken off, that I might be graffed in.
20 Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear:
21 For if God spared not the natural branches, take heed lest he also spare not thee.
22 Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off.
23 And they also, if they abide not still in unbelief, shall be graffed in: for God is able to graff them in again.
24 For if thou wert cut out of the olive tree which is wild by nature, and wert graffed contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be graffed into their own olive tree?
25 For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.
26 And so all Israel shall be saved: as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob: KJV
John 15:1-6
5:1 I am the true vine, and my Father is the husbandman.
2 Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit.
3 Now ye are clean through the word which I have spoken unto you.
4 Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.
5 I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing.
6 If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned. KJV
Happy new year