"Messianic Jew" refers to a Jew who follows the Messiah, while "Messianic Judaism" refers to the sect of Judaism that follows the Messiah, so in that regard, the earliest Christians before the inclusion of Gentiles in Acts 10 were all Messianic Jews who practiced the religion of Messianic Judaism.
Paul also said in Romans 3:31 that circumcision has much value in every way, so the issue with that and 1 Corinthians 7:19 is that circumcision conditionally has value if someone obeys the Torah, and the way to recognize that a has a circumcised heart is by observing their obedience to it, which is the same way to tell for a Jew (Romans 2:25-26, Deuteronomy 10:12-16). In 1 John 2:6, those who are in Christ are obligated to walk in the same way he walked, and he walked in obedience to the Torah.
A body can have many different parts, but that is not contrary to its unity.
Christ set a perfect example for us to follow of how to practice Judaism by walking in sinless obedience to the Torah, and as his followers we are told to follow his example (1 Peter 2:21-22), the label of "Christian" no longer refers to someone who refers to someone who follows Christ's example of practicing Judaism in obedience to the Torah, so if I use that label to refer to myself, then I am communicating something that is false about what I believe, so I need to use a different label to more accurately communicate what I believe, which is not intended to be an insult to the contributions of Christians.
The Bible clearly refers to people who are Jews, Greeks, males, females, slaves, or free, and Paul specifically identified as a Jew on two occasions, so he was not denying the reality of these distinctions, but rather he was denying that they gave someone a higher status when it comes to being in Christ.
While that is the case for some, there are many who authentically seek to practice Messianic Judaism as it was practiced by the earliest Christians.