Well, a quick check indicates Alkan wrote one prelude titled "Ancienne melodie de la synagogue" and another called "Psaume 150me," so he did try occasionally.

Yeah, "Mass" is a tough sell as Jewish, but only slightly less so as Catholic! I think Bernstein cared about creating consciously Jewish music (like with the Kaddish Symphony), though, while Copland was striving to be American more than anything.

Spanish and "Spanish" music present some of the same issues. What's more quintessentially Spanish music than Carmen? It's a different manifestation of the Orientalist impulse, maybe.