Unity of the Church
"He [Peter] said to them: 'You are well aware that it is against our law for a Jew to associate with a Gentile or visit him. But God has shown me that I should not call any man impure or unclean" (v. 28).
The story in Acts 10 and 11 of the conversion of Cornelius involves some telling features and some interesting subtleties. First of all we should bear in mind that Cornelius was already a heaven-bound believer. He was an old covenant, God-fearing Gentile believer. In the old covenant, circumcision into the priestly nation of Israel was not necessary for salvation, and there were many Gentile "God-fearers." In a sense, there were two churches in the old covenant: an inner core church of circumcised priestly people, and an outer circle of God-fearers.
Second, when Peter says in Acts 10:29 that it is "against our law for a Jew to associate with a Gentile or visit him," he was not referring to God's law but to the corruptions of the Jewish oral law traditions. God never put any roadblocks in the way of Gentile conversion in the old covenant. God welcomed Gentiles at His tabernacle (Numbers 15:14–16; contrast circumcision and Passover, which were only for Israel, Exodus 12:43–49).
Third, though Peter and the Jews regarded the Gentiles as unclean, the Bible never calls any human being unclean. Under the Levitical law you did not contract ceremonial defilement from touching or even marrying a Gentile. The idea that Gentiles were unclean was a sad perversion of God's law by Jewish tradition.
Thus, if Peter had been faithful to the Old Testament law, he would have had no reservations about going to Cornelius's house. God's acts recorded in Acts 10 and 11 reinforced something Jesus said over and over again: The Jewish oral law tradition was an evil perversion, and was to be rejected completely.
Since Cornelius was already a believer, Peter needed to accept him and proclaim to him the Good News of the new covenant. But there was a change in the new covenant. Under the old covenant there was a "wall of partition" between the inner circle of the Jews and the outer circle of the Gentile God-fearers. Now, however, all believers are in the innermost circle, a point made clear to Peter when the Holy Spirit baptized Cornelius, a point affirmed by Peter when he baptized Cornelius with water.
Coram Deo
Jesus assailed the notion that there is an oral tradition next to the written Bible, having equal authority. The Reformers took up the same fight against the oral tradition espoused by Roman Catholicism. Consider whether you or your church have constructed any such "oral traditions" which may not be supported by Scripture.