I wouldn't presume to speak for him, but I saw Shalom's words as saying we can define "who is a Jew" by looking at what he is rather than what he's not. A Jew is a descendant of a Jewess, or a person who has undergone an Orthodox conversion.
Correct
and who remains true to Judaism.
Not quite. A Jew is always a Jew no matter what. I am my mother's son - I can't change that. But I could be disinherited by the family (I'm not.). There are those who are 'separated from the people' for various reasons. They are Jews - but they are without a people. The final decision of expulsion or reuniting is left up to a Bet Din (court) of their community.
Christianity doesn't come close to being true to Judaism. Neither does Buddhaism. Nor does Islam.
Of the three you mentioned, Islam is the closest to Judaism in as much as like Judaism, it is a pure monotheistic religion which does not permit any visible representation of G-d. Buddism on the other hand is a g-dless religion - so it might be perfectly ok for a Jew to practice certain pehaviors of Buddism such as relaxation techniques or anything else which would not require idolotrous behavior. Even then it is always good for a Jew to check with their local Rabbis for confirmation - as I did before I started practicing Thai Chi.
The reason I asked that we consider a Jewish convert to Christianity as a Christian, is to avoid someone from thinking that Messianic Judaism is a recognized sect of Judaism. Or to quote something as being Jewish just because it was a comment from a Christian who happend to be a Jew. Jews have believed and not believed a number of things over the centuries. The fact that one Jew jumps into the Red Sea does not mean this Jew should jump. Hope that covers that point.
I also avoided answering the initial question because it is not my place to determine who is a Christian. I have heard a number of denominations attempt to state what is the minimum a Christian must do or believe etc. to be considered a Christian. Therefore, I was also being a bit "tongue-in-cheek." when I said Christians are the ones to make that decision. So far, I don't think there is one universal rule that covers all Christians on what is a Christian.
So if you tell me your a Christian - ok, your a Christian. Its that simple for me.
Shalom