I dug into this with Snow's SCSI trace and the 4.0 driver.
Apple CD-ROM 4.0 (DRVR 32 ".AppleCD", from CD-ROM Setup.image on the 7.1 CD) checks two things when it probes a drive:
1. MODE SENSE page 0x30 has to come back with 'APPLE COMPUTER, INC '.
2. The 16-byte INQUIRY product field has to be one of exactly three strings: CD-ROM CDU-8001, CD-ROM CDU-8002, CD-ROM CDU-8003. They are at offsets 0x47FC, 0x480E and 0x4820 in the DRVR
Snow reports CD-ROM CDU-800
4. That model only shows up in the later 5.x driver, whose table added 8004, 8005, CR-8004 and CDR-8004. So 4.0 rejects the drive.
I reproduced it in Snow on a IIcx with the real System 7.1 CD as the media:
- 7.0.1 + Apple CD-ROM 4.0, product CDU-8004: doesn't mount.
- 7.0.1 + Apple CD-ROM 4.0, product CDU-8003: mounts.
- 7.5.3 + Apple CD-ROM 5.3.1: mounts either way.
CDU-8003 is in both extensions - fixed here:
https://github.com/twvd/snow/pull/371