APFS disk plugged in newer system gives "Incompatible Disk" warning in original OS

Solution 1:

The newer versions of macOS have the root volume composed from a read-only volume and a read/write volume. The older versions of macOS have not been patched with software to correct interpret this type of configuration. Instead, these older versions have at least been patched to recognize the newer configuration exists and to display the warning message posted in the OP's question.

I have a 2018 Mac mini with Mojave installed on the internal drive. The external Thunderbolt 3 drive has both Mojave and Big Sur installed in the same APFS container. Furthermore, internal Mojave has the home directory for each account manually set to the home directory of the corresponding account on the external Mojave volume. (The external Mojave has the home directories in the default location.) When booting the internal Mojave, the warning message is displayed. This configure has been in use since Big Sur was released and no one has noticed any problems.

In other words, read and writing† to a APFS volume in a APFS container with a newer version of macOS apparently does not create problems. However, you would not want to use an older version of macOS to verify or repair an APFS container with a newer version of macOS installed.

IMO, if I was to remove Big Sur from the external drive, then I would still want to use tools from Big Sur or newer to verify or repair the APFS container which contained Big Sur. I think this would be good practice for macOS or any other operating system.

† Here I assume the write would be to a safe location. For example, while booted to Mojave, copying a file from a Mojave users desktop to a the same users Big Sur Desktop folder.