The idea that "messianic jews" use to promulgate the notion that one can be Jewish and another religion at the same time is based on the fallacy that there is a "Jewish race"- there is no such thing as a Jewish race. The idea of a Jewish race is a construct of the Nazis, part of their propaganda effort to justify their oppression and later extermination of the "Jewish problem". Think of it like this- if Jews are race, and one that is contaminating others because they are inferior- then the only way to protect the "superior" races is to kill the inferior one (and yes, this was a sick extension of Darwin's theory of evolution and Herbert Spencer's "survival of the fittest"- neither of these two had anything to do with the insane twist put onto their theories). Likke the Nazis, "messianic judaism" and its adherents seek to destroy Jews and Judaism- the Nazis tried to kill us ohysically, the "messianic jews" by redefining Judaism into yet another Christian sect and destroying Judaism spiritually,
The reality is that from the very start there has been no such thing as a Jewish race. In the Torah, it is understood that Yitro (a black Ethiopian), Moshe's father-in-law, converted to Judaism. When the Jews left Egypt the eruv rav (mixed multitude) left with them. By the end of the 40 years in the desert, the eruv rav had dissapeared- either having converted or left to go their own way once free of Egypt. So, even as they entered Israel for the first time behind Joshua, there was no Jewish race- but already a collection of ethnicities, races etc.
As for religion, a Jew that converts to any other religon ceases to be a member of the Jewish community. The Torah makes this point very clearly when it gives the laws of the Korban Pesach.
Shmot (Exodus) Chapter 12
43. The Lord said to Moses and Aaron, "This is the statute of the Passover sacrifice: No estranged one may partake of it. ??. ????? ?????? ?? ??? ????? ??? ??? ???? ?? ?? ??? ?? ???? ??:
So it starts off the list of those not allowed to eat of it with the 'estranged one" i.e. the Jew who has changed to another religion
After listing others, allowed and disallowed from eating the Korban Pesach it states:
47. The entire community of Israel shall make it. ??. ?? ??? ????? ???? ???:
In other words- the Jew who has converted to another religion is explicitly excluded from the community of Israel - they are not part of Bnei Yisrael, they are not Jewish!
When it is said a person remains Jewish regardless of converting, that is actually a statement to their detriment. The full statement should be- "a person remains liable to be judged under Jewish law even after converting to another religion." Thus a Jew who follows another religion would be punished with kares (spiritual excission) after death for being an apostate and abonding Judaism.
Despite all this, "messianic jews" try to claim they are Jewish. Why? For a very simple reason- they are a Christian missionary movement that is using lies, deceit and a "bait and switch" scam to try and convert Jews to Christianity. They are actually not that succesful- by their own admisson at most 20% of people in "messianic jewish" communities have even a tenuous connection to Judaism- and many of those are not Jewish by Jewish standards. External estimates put the number at under 10% with even a tenuous connection to Judaism- and only a tiny fraction of those are Jewish by Jewish standards (i.e. a Jewish mother or a valid conversion to Judaism)
Whats the difference between "messianic jews" and Christians- nothing- they are a Christian sect using the trappins of Judaism and nothing more