I disagree Gentiles are not under the law of Judaism. If we were obligated to walk exactly as Christ did then we would be obligated to make sin offerings, keep all the Sabbath days, observe the Passover, and the dietary laws, and be circumcised just as he did. None of these were ever commanded in the New Testament and if the requirements for God’s covenant haven’t changed then there is no New Covenant.
In Deuteronomy 10:12-16, God wanted His people to obey His commandments and circumcise their hearts. In Deuteronomy 30:1-8, it prophesies about a time when the Israelites would return from exile, God would circumcise their hearts, and they would turn to obedience to the Torah. In Ezekiel 36:26-27 and Jeremiah 31:33, the content is in regard to the New Covenant and the Israelites returning from exile, where God would take away their hearts of stone, given them hearts of flesh, and send his Spirit to lead us to obey the Torah, and where he would put the Torah in our minds and write it on our hearts, so they are describing God circumcising our hearts by means of the Spirit. In Romans 2:25-29, the way to recognize that a Gentile has a circumcised heart is by observing their obedience to the Torah, which is the same way to tell for a Jew, and circumcision of the heart is a matter of the Spirit, which is in contrast with Acts 7:51-53, where those who have uncircumcised hearts resist the Spirit and do not obey the Torah. So the New Covenant is all about returning to obedience to the Torah.
In Matthew 4:15-23, Jesus began his ministry with the Gospel message to repent for the Kingdom of God is at hand, which was a light to the nations, and the Torah was how his audience knew what sin is (Romans 3:20), so repenting from our disobedience to it is an integral part of the Gospel message, which he prophesied would be proclaimed to all nations (Matthew 24:12-14). Likewise, in Acts 2:38, when Peter told his audience to repent and be baptized for the forgiveness of sin, the Torah was how they knew what sin is. In Romans 15:4, Paul said that OT Scripture was written for our instruction, and in 15:18-19, his Gospel message involved bringing Gentiles to obedience in word and in deed, so he was on the same page in regard to teaching repentance from our sin. So yes, the NT does call for us to repent from our sin, which is the transgression of the Torah (1 John 3:4), which included repenting from things like breaking the Sabbath or other holy days and from eating unclean animals. Gentiles can look at the Torah that Jesus taught by word and by example and decided whether or not to follow him, but Gentiles can't follow him by refusing to follow what he taught.
God's nature is eternal, so the way to act in accordance with His nature is therefore also eternal, and if that were to change under the New Covenant, then God's nature would not be eternal, and the only way that we should no longer follow these laws is if what they teach us about God's eternal nature if no longer true of God. For example, in 1 Peter 1:16, we are told to have a holy conduct for God is holy, which is a quote from Leviticus where God was given instructions for how to have a holy conduct, which includes keeping God's Sabbaths holy (Leviticus 19:2-3) and refraining from eating unclean animals (Leviticus 11:44-45). The only way that we should no longer have a holy conduct as God is holy is if God is no longer eternally holy, and when Gentiles refuse to have a holy conduct as God holy, they are bearing false witness against God's holiness. In 1 Peter 2:9-10, Gentiles are included as part of God's chosen people, a holy nation, a royal priesthood, and a treasure of God's own possession, which are terms used to describe Israel (Deuteronomy 7:6), so Gentiles also have the delight of getting to obey the instructions that God gave to Israel for how to fulfill those roles. It would be contradictory for a Gentile to want to become part of a holy nation while wanting nothing to do with following God's instructions for how to live as part of a holy nation.