We've been able to re-enable Offline Files.
We had this problem with 4 of 10 v2004 PCs. With one, the user could log on without BSOD'ing but it would BSOD upon browsing a network drive. The rest BSOD'd during logon until I disabled Offline Files via remote registry edit. The other 6 are getting along just fine so far.
In all 4 cases, we've worked around it by resetting Offline Files (create a FormatDatabase DWORD value set to 1 in HKLM\System\CurrentControlSet\Services\CSC\Parameters, re-enable Offline Files service and reboot the computer). Then the users can log on with Offline Files enabled.
However, the mapped drive (which maps to a DFS share, if that's relevant) is inaccessible after logon. The workaround for that has been to add a logon script that unmaps the drive, then remaps it to the non-DFS share. Initially, only the redirected folder share (also DFS) is browsable. Later, the rest of the DFS shares become browseable, perhaps after they're onlined by Offline Files.
Small sample size. Don't know how universal this workaround is, but hope it helps somebody!
Thanks for this tip, I've just managed to re-enable offline files on one of my PCs by following this. Weirdly though, File Explorer won't resolve the name of the device where the share is hosted - I can ping it by name and I can access other shares by name, but I've had to change my shortcuts to use the IP address instead.