I’ve been teaching on the Book of Acts this semester, and Christoph Heilig gives a good summary of Acts 10-11:
To sum up, we find in Acts 10–11 the recognition by Peter that it is wrong to assume moral impurity and profaneness for Gentiles per se. Rather, they can become members of the messianic community by repentance and faith, with-out becoming Jews. As Peter says later (Acts 15:8), God knows the repentant heart and purifies it through faith without making a distinction between Jews and Gentiles (Acts15:9); both are saved in the same way (Acts 15:11). This implies that even before conversion it would be unfair to treat uncircumcised people as more morally impure and profane than unbelieving Jews. The way Peter counters the objections regarding his association with Gentiles, who became Gentile believers, strongly indicates that the equal status confirmed by the Spirit has implications in two directions: (a) It exempts the new members of the messianic community of any moral suspicion that would have justified doubts about having,e.g., a common meal; (b) at the same time it makes clear that these Gentiles are set apart for being told “the word” so that they are on the same level as Jews who have not yet responded positively to the Christian proclamation. As Dunn points out, “Peter was now free to deal with Cornelius as he would have dealt with any fellow Jew.”