God has always been holy, righteous, and good, so He has always had such a conduct, and His law is holy, righteous, and good (Romans 7:12) because it is based on His character and it is His instructions for how have such a conduct. So the way to do what his holy, righteous, and good existed from the beginning independently of any covenant and would exist even if God had made no covenants with man, so having such a conduct is about identifying with God, not a specific group of people. Anyone who identifies as one of God's chosen people through faith in Messiah, who has faith in Him for how they should live, and seeks to do what is holy, righteous, and good should follow the instructions that God has given to His people for how to do so. According to Deuteronomy 7:6, Israel is God's chosen people, a holy nation, and a treasure of God's own possession and according to 1 Peter 2:9-10, Gentiles are included as being part of that, so it is not just Israel that is to be set apart. Jesus always kept the Sabbath, and all who identify as his followers who abide in him should follow his example (1 Peter 2:21-22), should walk in the same way that he walk (1 John 2:4-6), imitate him (1 Corinthians 11:1), and be like him (Philippians 2:5), not leave all that for just the Jews to do.