Jesus is reported to have said of Peter something like you are the rock upon whom I will build my church. How does 'church' make sense to 1st century Jews? If Jesus the Jew never intended to establish a new religion, why church and not temple?

The Greek word used in that passage (Matthew 16:18) is ekklêsia, which means simply "congregation," a term Jews often applied to their own faith communities (e.g. the word appears in reference to Jewish congregations all throughout the Greek translation of Deuteronomy, for example). That statement from Jesus, however, does only make sense if indeed Jesus intended to found a new faith community of Jews. More likely the statement was invented after the fact and only attributed to Jesus to justify the church hierarchy then arising.