Mounted volume not accessible
Finally, after many turns, I've found what's going on: 

The executing shell/app in the script (e.g. zsh, sh, python - in my case /bin/bash) needs to have Full Disk Access privileges. In order to do so I went to Apple Menu > System Preferences > Security &amp; Privacy, selected Privacy tab, unlocked the settings and added /bin/bash to the list.

Now I can read and write the mounted share.