This chapter always brings up the idea that God has “freed” the Jews – and everyone else – from having to obey the dietary restrictions in the Law. I have posted a separate topical study about clean and unclean foods, examining each occurrence of the subject in the New Testament, and whether that is what THIS chapter of Scripture is teaching. I do not believe it is.
Furthermore, I do not agree that the Scriptures teach that the death of Jesus and His resurrection has “freed” us from obeying God or His commandments. First, I just want to point out, that this incident took place 3-1/2 years after Jesus rose from the dead. In those 3-1/2 years, Peter continued to obey the dietary laws. Notice he says that he has never eaten anything common or unclean? He is going by the definition of clean and unclean food, given in the Torah (Lev 11). The resurrection of Jesus did not change Peter’s eating habits. If the theology is, now that Jesus has been crucified and raised from the dead, the Law has been done away with and Jesus has declared all foods clean, what was Peter doing still obeying the dietary laws for 3-1/2 years?
He continued in the dietary law because Scripture is very clear that believers are to continue to obey God and His commandments (Jer 31:33, Eze 36:25-27, and many other places in the Old Testament, Joh 14:15, Rom 3:31, and many other places in the New Testament).
But His death and resurrection has freed us from earning our salvation by obedience to the Law (Gal 2:16). (In fact, Moses does not teach that the purpose of the Law is to earn salvation, see God’s word gives life to those who find it.) Praise God! The death and resurrection of Jesus has freed us from the penalty disobedience to the Law earns for us, which is death (Rom 2:12-13, 3:21-26). This is an important distinction, because a belief that Jesus has “freed” us from obedience to God’s will as expressed in the Law (Mat 7:21-23, Rom 2:17-20, 1 Joh 3:4) has opened the door of acceptance in the Church for all manner of unrighteous behavior which is condemned in the Law.
So Peter then tells the household of Cornelius in this chapter in Acts, that the Lord showed him (using the vision of the great sheet) that He had cleansed all men (i.e., the Gentiles, Act 10:28), and that Peter was no longer to consider any man unclean for a Jew to associate with. The vision did not mean that all animals were now fit to eat, but that all men were now clean in God’s sight.
The Jews did not associate with Gentiles, because Gentiles were pagan idolaters, and idolatry was abhorrent to them. But now, God extended salvation to the Gentiles. A saved Gentile is not a pagan idolater. We know this is the correct interpretation of the vision, because while Peter was preaching, even before he got to the altar call, the Holy Spirit fell on all the Gentiles present, and Peter knew it because they started speaking in tongues, as Peter and the rest of the disciples had on the Day of Pentecost in Acts 2.
FYI, the salvation of Cornelius, and the opening of the door of ministry to the Gentiles, heralds an important fulfillment of prophecy (please see daniel 9 and the abomination of desolation series).