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In the LW's own words, "my conclusion has been that god probably exists (but doesn't really play any sort of essential role in my life and is just some sort of vague entity out there)"
Yet in the very next paragraph, she claims that "my Jewish religion/culture was important to me."
These two statements are so utterly irreconcilable that they lead me to think the LW has very little respect for her own religion. If she did, she might spend some time reading her own holy book, and realize that the god described in the Old Testament is certainly not just some "vague entity out there," but a very purposeful and well-defined being who demands that his people obey very specific sets of instructions about how to live our lives.
It certainly sounds as though the LW's Jewishness is more a matter of style than substance. She's more concerned about how her husband looks to the rest of the congregation than she is about understanding the core tenets of her faith. In fact her husband, by refusing to pretend to be something he's not, is showing more respect for that faith than she is.