You teach a works salvation !
Cornelius was a Gentile and Gentiles did not do circumcision, as commanded by God, and so in this, they did not obey God.
There is The Law in the Old Testament, The Law that consists of sins not to do, and of good to do, and then there is the works of the law, both together called The Law.
Gentiles did not do the works of the law, the WORKS of the law does not just mean not to steal, commit adultery, etc., the works of the law were circumcision, it is a written code with regulations, for worship, and an earthly sanctuary. Gifts and sacrifices were required for worship and the earthly sanctuary. They are only a matter of food and drink and various ceremonial washing---external regulations.
God forgave us all our sins, having canceled the written code, with its regulations, that was against us and that stood opposed to us; he took it away, nailing it to the cross.
Therefore, we are not to let anyone judge us by what we eat or drink, or with regard to a religious festival, a New Moon celebration, or a Sabbath day. These are a shadow of what were to come; the reality, however, we find in Christ.
On the Sabbath day, the law said that no one could work, not to even lift objects. Do you see the correlation from Sabbath day no works to no works for being saved? Jesus is our Sabbath rest, we are saved by faith, and not of by works. A NO WORK rule was in place for the Sabbath day. Just like we are saved by faith and NO WORKS; however, Jesus says it is UNLAWFUL to do evil on the NO WORK day of the Sabbath, and Jesus said it was LAWFUL to do good on the NO WORK day of the Sabbath, see Luke 6:9. For people to misconstrue that no work means we do not have to repent from doing evil before Jesus saves us is absurd. Jesus tells us to believe and repent, Matthew 4:17. God knows are hearts and if we are truly contrite, Acts 15:8. The message that saves is a message that says Jesus died for sinners, Acts 11:14. If we hear the message that saves, yet do not believe we are sinners and need to stop sinning, then God will know this.
BEY God. Again, the Gentiles did not obey God with circumcision. When I was a Catholic I feared God, but did I obey God? I obeyed what the Catholics taught. I did not have Jesus revealed to me UNTIL I had the teachings of Jesus and obeyed. In the old covenant, God's word said be physically circumcised, and in the new covenant, there are new things we are told, and we are told to obey, and what are we to obey? The scriptures tell us we are to confess and call on the name of the Lord. "If anyone loves me he will obey my teaching. My Father will love him, and we will come to him and make our home with him.