It might be useful, in both cases, to distinguish "fans" and "consumers" of those styles. Yes, the people who most consciously identify as fans of the styles are picky, but I'd be willing to bet that the vast majority of classical play counts by volume are consumed for muzakish purposes. Mozart for babies, Vivaldi for malls, etc.

The same may be true for Jazz, though in that genre there may be a bit more of a separation between jazzy background mood music and jazz as consumed by fans. There are some overlaps ("The Girl from Ipanema", "Take Five", etc), but they may not be quite as central to the canon as their classical counterparts.