Messyonic "judaism" is NOT Judaism. It is a cult preying on the poorly educated Jew who doesn't know Judaism very well and is therefore vulnerable to someone telling them untruths. Messyonic "judaism" does not in any way speak for actual Jews, since it's made up of mostly non-Jews. So crowing that Messyonic "judaism" acknowledges anything is absolutely meaningless as far as actual Jews are concerned. Catholics have their beliefs, and fine. Jews have their own beliefs, and don't require tenets from other religions.
I know a former Jew who called himself a Messianic Jew. He is now a Christian minister.
The first followers of Jesus were Jewish, and they didn’t view their actions/faith as “un-Jewish”. They believed He was the Son of God they’d been expecting (as Jews) for thousands of years. They had a succession of prophets proclaiming He would come, and after He came there were no more prophets. My understanding is that Messianic Jews simply looked back and understood why the prophets stopped coming.