Is there a way to hook up my SNES to a modern A/V receiver?

Your best option is to get an SNES/N64/GC S-video cable, and use a third-party s-video to component adapter.

The system came with a stereo A/V cable (red/white/yellow), and Nintendo also sold a first-party S-Video cable. SNES, N64, and GC used the same multi-out port, so if you have trouble finding an SNES S-video cable, try searching for N64 and GC S-video too. (GC also had a separate port for component video output.)

Note: the multi-out port on the smaller, redesigned SNES model will not work with the S-video cable. If you only have the redesigned system you'll need to use a composite-to-component adapter instead.