I would describe what I’ve read of Ray Bradbury’s as science fiction, rather than fantasy. How the author would identify “Jewish,” I do not know, but a case might be made that there’s a Jewish cultural mindset, irrespective of religious belief, that could affect approaches to literature.
It was a loaded question. I think the "blurring" of the 2 genres you mentioned is a matter of readers/viewers/marketers doing the blurring, not the authors.
Bradbury considers himself a fantasy writer: . "I've only done one science fiction book and that's Fahrenheit 451, based on reality. Science fiction is a depiction of the real. Fantasy is a depiction of the unreal. So Martian Chronicles is not science fiction, it's fantasy. It couldn't happen, you see? That's the reason it's going to be around a long time—because it's a Greek myth, and myths have staying power."
I've been a fan of both forms for 50 years and I think most of the writers would agree with Bradbury's definition. Marketers like the Sy Fy Channel have twisted definitons beyond logic. To them horror, corny science fantasy, gory slasher junk etc. all qualify as "Sci Fi" (sorry, it's been dumbed-down to Sy Fy).
As to the matter of Jewishness, I agree with you. But as I read it the author seemed to be referring to fiction from a mainly religious perspective, i.e. Lewis and Tolkien. It's an interesting question. Ellison's Jewish but he's sure as hell not very religiously-oriented.