I've edited anydesk config file:
sudo vi /etc/anydesk/system.conf
changing value of one of its parameters from 0 to 1:
ad.security.interactive_access=1
Opened Anydesk by unprivileged user
As a result, it became enabled:

Updated: In current Anydesk 5.5.5 version run in terminal:
$ anydesk-global-settings
Then enter your current user password and set Unattended access. Now it saves it.
I think you should remove .exe and use sudo (tested at least on ubuntu 20.04)
# echo my-new-password | sudo anydesk --set-password
This worked for me: Setting the password using the command line https://support.anydesk.com/Command_Line_Interface
echo mynewpassword | sudo anydesk --set-password