In Acts 6:13, Stephen was falsely accused of teaching Jews against obeying God's Law, and in Acts 21:20-24, Paul took steps at the direction of James to disprove a false rumor that he was teaching Jews against obeying God's Law, so if no one in leadership was doing that, then all Christians were Torah observant Jews for roughly the first 7-15 years after Christ's ascension up until the inclusion of Gentiles in Acts 10. So these were the first Messianic Jews. However, Jews who do not recognize Jesus as their Messiah consider Jews who do that have gone after a false prophet, so they are shunned. According to Deuteronomy 13:4-5, the way that God instructed His people to tell that someone was a false prophet, even if they performed signs and wonders, was if they taught them against obeying what God had commanded them. So Christians who teach that Jesus did away with the Law are essentially teaching that he was a false prophet.
However, Messianics recognize that that Jesus did not do away with the Law, but rather he set a perfect example for us for how to walk in obedience to the Law, and we are told to follow his example (1 Peter 2:21-22) and to walk in the same way that he walked (1 John 2:3-6). We also recognize that following Messiah's example is not just for his Jewish followers, but also for his Gentiles followers, so Messianic Judaism includes Gentile believers who seek to follow what Christianity was at its origin, which was a sect of Judaism. Over time, Christianity has sadly become separated from the Jewish roots of its faith, with Christians following the Messiah, but not God's Torah that he walked out, with Jews following God's Torah, but not their Jewish Messiah, and with both only following half the truth. The Torah is the way (Exodus 18:20, Deuteronomy 5:33, Deuteronomy 8:6, Deuteronomy 26:16-17, Deuteronomy 28:9, Isaiah 2:3, Jeremiah 6:16-19, Psalms 119:1, Matthew 3:3, Matthew 22:16), the truth (Psalms 119:142, Psalms 119:151, John 17:17), and the life (Proverbs 13:14, Matthew 19:17, Deuteronomy 30:15-20), Jesus is the way, the truth, and the life (John 14:6), the Torah is God's Word, and Messiah is God's Word made flesh, so trying to separate one from the other will leave you with only half the truth.