Dear moderator,
I'm impressed with your work. As you mentioned, it's quite a strong statement that, although many differences of opinion about Judaism exist among Jews of different observance levels, the one thing on which we all unequivocally agree is that we do not worship Jesus or any other idol (not even Elvis). Considering the sometimes vast differences that can occur between very traditional Jews and Reform Jews, that one agreement (among others, of course) is quite firm.
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But you have no right to determine the religious identity of another faith group
That's the crux of the entire issue. If anyone did it to Christians, you can just imagine the uproar.
Think about a female body. It possess a few of the same body parts as men: nose, eyes, arms, legs, and so forth. With the logic that the messies use (they accept or share "some" of Judaism, but not all), a woman can therefore say that she is a male, simply because she shares some of the same biological components.
If messies reject one of the most defining aspects of Judaism and still insist on calling themselves Jews, then females can lack one of the most defining aspects of males and still call themselves males. Isn't this all absurd?