Thanks phreakout! After messing with it some more, believe it or not, I think it's a software problem. If I boot the SE/30 from a System 6 floppy, then it recognizes other floppies when they're inserted just fine. But if I boot from System 7 on the hard drive, it behaves as I originally described, and ignores inserted floppies. This is true both for floppies I make from my PC, and vintage Mac-formatted floppies.

I'm thinking maybe this is a problem with Disinfectant, which is installed. I assume it patches the floppy insert handler to check for viruses, and maybe it's screwed up somehow.

I would test this theory further by disabling Disinfectant, but now the SE/30's hard drive appears to have disappeared! When I load some SCSI utility software from a floppy, it doesn't even show any drives on the SCSI bus, just the computer itself at ID #7. Not good!