My goodness, Bruce has NEVER identified as Jewish nor have others identified him as such in the comics. He doesn't want to be Jewish (as far as we know). Even if his parents had lived there is no evidence they would have raised him Jewish. He is NOT JEWISH regardless of what his mother was matrilineal descent be damned. This he is Jewish because his mother was Jewish argument is the same as the asinine "One Drop" Laws of the Deep South. Let it go, Batman is NOT JEWISH, nor has he been presented as such during the entirety of his eighty-plus year history, regardless of how much you want him to be.
Edit - I'm not going down this rabbit hole again. I have better things to do than relitigate this closed case. I will not post another post in here. I'm done with the thread.