Jaime,In what sense do you think the circumcised believers meant
Acts 11:18 When they heard this, they had no further objections and praised God, saying, “So then, even to Gentiles God has granted repentance that leads to life.” ?
Bear in mind they did accept this.
Acts 11: ["17a & 17b MINE]8 But I said, ‘Not so, Lord! For nothing common or unclean has at any time entered my mouth.’ 9 But the voice answered me again from heaven, ‘What God has cleansed you must not call common.’ 12 Then the Spirit told me to go with them, doubting nothing. Moreover these six brethren accompanied me, and we entered the man’s house.
15 And as I began to speak, the Holy Spirit fell upon them, as upon us at the beginning. 16 Then I remembered the word of the Lord, how He said, ‘John indeed baptized with water, but you shall be baptized with the Holy Spirit.’ 17a If therefore God gave them the same gift as He gave us when we believed on the Lord Jesus Christ, 17b who was I that I could withstand God?
Peter particularly stressed God's initiative
in Acts 11:8, 9, 12, 15-17a, as well as his own inability to withstand God in Acts 11: 17b).
Acts 11:14 who will tell you words by which you and all your household will be saved.
Cornelius and "all" his "household" were not "saved" from God's wrath until they heard and believed the gospel of Jesus Christ that Peter proclaimed to them (v. 14).
Acts 11:16 Then I remembered the word of the Lord, how He said, ‘John indeed baptized with water, but you shall be baptized with the Holy Spirit.’
Clearly the baptism of the Holy Spirit is what he referred to in verse 16.
Peter identified "believing in the Lord Jesus Christ" as the only necessary prerequisite to receiving the baptism of the Holy Spirit (v. 17a).
Now, going back to v.2-3, it shows here that those of the circumcision contended with him, concerning his eating with the Gentiles. In verses 4-18, Peter explains. And by appealing to what God had done (v. 17a), he justified his eating with Gentiles in Caesarea.
The subject verse 18, shows that Peter's explanation was satisfactory to his critics. His Jewish brethren agreed that God was saving Gentiles, by granting them repentance. And that, for that matter, is of repentance to life.
This is the point in scriptures where the truth of the matter that salvation is not only for the Jews, but for the Gentiles as well. And that, in the same way as for the Jews, by repentance towards God and faith in the Lord Jesus Christ.
What can be seen in the case of Cornelius and his household, is that, they believed the words they heard from Peter about Jesus, that even before confessing that with their mouth and even before they were baptized, they were saved. And that is clearly evidenced by the Lord Jesus Christ's baptizing them with the Holy Spirit. They were saved, and were baptized with the Holy Spirit because they repented unto believing in the gospel of Jesus Christ.