Virtually all of Judaism is messianic in that it anticipates the moshiach, or the "annointed one" who, in the line of David, will establish in Jerusalem, the religious focus of the world of both for Jews and gentiles (Isaiah 2:2-4; 11:10; 42:1) with no expectation however, that this person will be in any way more "divine" than anyone else.
That concept has meaning integral to Judaism itself, as the "Chosen People".
Whereas I think its in Galations where Paul admonishes his readers that there is neither gentile nor Jew, male nor female - at least in his conceptualization - but they are all one in the lord, Jesus. The term, "Christian" in Acts is first used in Antioch, probably ~80AD, and from thenceforth has been broadly used to ascribe subscription to Jesus dinity.
The meaning of words matters. At least to me.
By declaring oneself to be a Messianic Jew, one is saying that they still honor their Judaism as well as the Christ who completes it. You shouldn't feel slighted in that. It is a huge deal for any Jew to accept Christ as Lord and Savior, because to do so, it usually means that they become ostracized and disowned by their entire families. I don't see your average Gentile having to put up with that.
>> “ with no expectation however, that this person will be in any way more “divine” than anyone else.” <<
Definitely not so. - Isaiah said that he would be Immanuel (God with us).
Yeshua is the sole purpose of all Hebrew worship. He is the Lamb of YHVH that takes the sin of the world.