Before I begin: I DID read the two stories you posted, and thank you. But my reply is to the paragraphs I’ve quoted.
1: Interesting distinction. I did know of the halachic definition of who’s a Jew (= if your mother’s Jewish - you are), but the main objection to Messianic Jews and Hebrew Christians I’ve heard from Rabbinical Jewish sources is that if one becomes a Christian (“Hebrew Christians” and “Messianic Jews” both included), one is not only an apostate, but one is no longer a Jew. How can this be, if Messianic Jews and Hebrew Christians are still considered “fair game” for prozelytizing?
2: Just to make sure I didn’t misunderstood what you wrote (probably did - since English is, as you know, not my mother tongue

):
Are you saying that conversion to Judaism is not a matter of salvation for Jews (the “…for us”-part?) or are you saying that Gentiles don’t need to convert to Judaism to be saved?
The latter would fit my understanding of what Rabbinical Judaism teaches better than the former, but I’ve been known to be mistaken, and I’ve heard that where 10 Jews are gathered, 11 opinions are voiced