I have to disagree. I could give you a whole list of scriptural references, but to what avail? It appears that you don't believe the NT writings, so it would be a waste of time for both of us.
Exactly. They are Christians and nothing else.
However, they call themselves Messianic Jews. I don't have any problem with that. Do you? If so, why?
Because a trinitarian belief which includes a human as God couldn't be more diametrically opposed to Judaism. As for Messianism, ("Messiah" being on who leads in saving the Jewish people, examples: Moses, Joshua, David etc.)Jews believe they have had Messiahs in the past and will have one or more in the future. Gods coming down from heaven is a concept that has its origins in earlier paganism and mystery religions which has nothing in common with Judaism.
Thats not to say the two religions do not have similarities. They both seem to realize the ideal successful society here would be based on observance of the 10 commands (words). A beautiful concept which spawned western civilization.