Here we see a reference to two different gospels:
"But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as the gospel of the circumcision was unto Peter" (Gal.1:7).
What was preached to the Jews during the Acts period? Here is what Paul preached to them:
"And straightway he preached Christ in the synagogues, that he is the Son of God...proving that this is the very Christ" (Acts 9:20,22).
The Apostle John makes it clear that those who believed that Jesus is the Christ, the Son of God, are "born of God":
"Whosoever believeth that Jesus is the Christ is born of God: and every one that loveth him that begat loveth him also that is begotten of him...For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith. Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?" (1 Jn.5:1,4,5).
John also made it clear that those who believe this truth receive life:
"But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name" (Jn.20:31).
This is the gospel or "good news" of Christ which was first preached to the Jews, the gospel which saved all those who believed:
"For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek"(Ro.1:16).
The heart and soul of the gospel which was preached to the Jews during the Acts period concerned the "identity" of the Lord Jesus. And while He walked the earth He said this to the Jews:
"And he said unto them, Ye are from beneath; I am from above: ye are of this world; I am not of this world. I said therefore unto you, that ye shall die in your sins: for if ye believe not that I am He, ye shall die in your sins" (Jn.8:23-24).
On the other hand, the heart and soul of the gospel of the uncircumcision concerns the "purpose" of the Lord's death upon the Cross:
"Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain. For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures" (1 Cor.15:1-4).
Two different gospels and belief in either of them brought salvation to all who believed.