How does Peter's vision in Acts relate to Paul's teaching about food offered to idols?
Peter's vision in Acts used the same analogy of clean and unclean foods, teaching him not to refuse what God created. Paul applies that grace-given freedom to marketplace food and unbelievers' feasts: eat without asking conscience questions, unless someone explicitly says the meat came from a pagan temple; then it differs.
Les explains that Paul's instruction tells believers to eat whatever is sold in the shambles or open market, asking no questions for conscience' sake, because the earth is the Lord's and the fullness thereof. He points to Peter's Acts vision as a glimpse of the same analogy: the "sheep" came down filled with all manner of four-footed animals and creeping things, and Peter was told to kill and eat. As a good kosher Jew, Peter refused, saying he had never eaten anything unclean. Les says the Lord was teaching Peter something totally different, but with the same analogy. Paul then brings the freedom grace gives even to the Jew: do not worry whether it is kosher; the Lord created it, thank the Lord for it and eat it. At a feast, eat what is set before you without questions for conscience' sake, but if the host says beforehand the meat came from the pagan temple, that makes it different.