Just as you are fully entitled to decide who is a Christian or not, we will decide who is a Jew or not. ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€š A Jew who trusts in Christ is still a Jew (provided his birthmother was a Jew or he underwent an orthodox conversion); he is a heretic, but he is still a Jew. ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€š However his beliefs are not Judaism.
Of course, the ultimate decision on who's who and who's what belongs to God. Whatever He decides will stand, no matter how we have identified or classified ourselves. He will separate the sheep from the goats, expose the wolves in sheep's clothing, and distinguish truth from error.
When it comes to identifying our Lord's disciples, I can eliminate people whose gross speech and conduct deny the Lord; but I can't be sure about all the people who claim to follow Him. St. Paul taught, "Some men's sins are clearly evident, preceding them to judgment, but those of some men follow later" ( 1 Timothy 5: 24, New King James Version ).
By God's grace, our overseers must decide which people to admit, ordain, discipline, or excommunicate. During our sojourn here, however, these decisions are effective only within the groups overseen. Regardless what our elders decide, outsiders and sometimes a few insiders may disagree. So, it's not unusual to find different opinions on who's a Christian and what's Christianity.
I think the same holds true for decisions on who's Jewish and what's Judaism. As a believer in the New Testament, I again follow St. Paul, who taught, "... He is not a Jew who is one outwardly, nor is circumcision that which is outward in the flesh; but he is a Jew who is one inwardly; and circumcision os that of the heart, in the Spirit, not in the letter; whose praise [ "Jew" means praise ] is not from men but from God" ( Romans 2: 28, 29 ibid ). The Orthodox Study Bible here comments:
2: 29 The name Jew is from "Judah," which means "the Lord be praised." A true Jew seeks only praise ... from God. ( A Gentile who keeps the natural law of the conscience is righteous and counted as a Jew.) The legalist's goal is vainglory, praise from men; the spiritual man, Jew or Gentile, has the goal of pleasing God. True circumcision, and true baptism, is of the heart, in the Spirit, leading from repentance to obedience.
Because I agree with all that and believe that Jesus is the Christ, I would say that Messianic Jews can live to God's praise and glory and that their doctrines and practices can be classified as a kind of Judaism. Of course, my opinions have no force.
When it comes to the terms "Orthodox Judaism," "Conservative Judaism," "Reform Judaism," "Reconstructionist Judaism," and "Messianic Judaism"; I think we're dealing with retronyms
, new words coined for an object or concept that's no longer unique. So, I wouldn't say that Messianic Judaism is Reform or Orthodox Judaism, but I do consider it a kind of Judaism.