You and I, Peter, are Jews, used to thinking of ourselves as categorically distinct from “Gentile sinners.” But we know (though conviction and experience) that a person (whether Gentile or Jew) is not considered of worth (“righteous”) by God through Torah-observance (“living Jewishly”), but through faith in (what God has done in) Christ. We look to God to consider us valuable (“righteous”) in Christ, not through obeying the Torah, and this is so even if (in situations like Antioch’s) our resulting behaviour makes us look like “sinners” (“living in a Gentile fashion”). Dos that mean that Christ has led us into sin? No way! Only if one were to reinstate the Torah as the arbiter of worth (“righteousness”) would “living like a Gentile” in Christ be classified as “transgression”. In fact (taking myself as a paradigm), I have died to the Torah - it is no longer what constitutes my standard of value - because I have been reconstituted in Christ. My old existence came to an end with the crucified Christ; my new life has arisen from the Christ-event and is therefore shaped by faith in the death of Christ, who loved me and gave himself for me. This divine gift I will by no means reject: if “righteousness” were measured by the Torah, the death of Christ would be without effect.