I need to qualify a few things to make sure I understand your position: " You can be Jewish without being a Jew". So one can be the adjective without inferring the noun?
They can have an element in them that is Jewish, but they need not be a Jew. So, the adjective requires a portion, but not the entirety, of the noun. Saying that the adjective and the noun are unrelated is ludicrous.

Now you admit that there is no consistent "Jewish" culture, but the claim is still appropriate because one can trace back to a common point of origin. Is that right?
"Admit" seems to imply that I recognize it as a weakpoint, although it is not a weakpoint. Essentially, though, your understanding of my position is sufficient for as far as we've gone.

This common point of origin would be appeal to Abraham or the introduction of Mosaic Law and its surrounding features? Would that be your view?
Yes, it is.

Regardless, the key it would seem is this point of origin. If I understood you correctly then it would seem Christians are also Jews as they trace back to that same point: accepting all the Old Testament as actual and authoritative. One might also argue Muslims are also Jews as they too recognize the Old Testament and trace back to Abraham.
Christians are not Jews. Because they have some Jewish elements does not make them Jews. Following that line, one who would argue Muslims are Jews would also be incorrect.

...more later, it's back to the slaving hell hole I go.