It is important to note that Peter was the man to whom Christ had given the “keys of the kingdom of the heavens” (Matt. 16:19-20). It should, consequently, be of little surprise to the reader that it was through Peter's delegated authority and instrumentality that the kingdom of God was “unlocked” to these God-fearing Gentiles. It also need to be noted that, although Cornelius was uncircumcised (and thus not a “full-fledged” proselyte of Israel), he was by no means representative of most Gentiles living during the time of the Roman Empire. Cornelius was “devout and fearing God with his entire house, doing many alms to the people [Israel] and beseeching God continually…a man just and God-fearing, besides being attested by the whole nation of the Jews” (Acts 10: 2, 22). It would seem that Cornelius was, in other words, a “foreigner” who had joined himself to the God of Israel, keeping Yahweh’s Sabbaths and holding fast his covenant (Isa. 56:1-8). He and his household recognized their place in subordination to the nation of Israel, and desired to worship the God of Israel via the mediation of Israel. Other examples of God-fearing “foreigners” like Cornelius would be the Roman centurion (referred to in Luke 7:1-5) and the Ethiopian eunuch (Acts 8:29-38).
Part Four: http://thathappyexpectation.blogspot.com/2016/10/a-study-on-two-evangels-part-4.html