Let's say I create a device which has an embedded Linux box in it (for example, a Raspberry Pi). After booting up, it starts the main application which is designed to provide the UI for the device.

The simplest way to produce more of them, is just to set up everything on one specific device, set the users, privileges, configure the booting process, install my software, and then create an image of the SD card. Installing that image to other SD cards gets me identical clones of the original device, which I can now ship.

However, this can lead to a serious vulnerability. As all the users will have exactly the same root password, all it takes is one user figuring it out (having access to the physical devices counts, as far as I know, for completely compromised security), and that one user might then use this knowledge to compromise the devices of other users (the device is expected to be used while connected to a network)

How can one mitigate this risk?

The software also needs to know the root password (as it needs to configure some hardware registers for the peripherals), so does this mean I have to compile the executable for each of the physical devices separately with separate root passwords, and create the users on each device separately, then manage to copy the correct software to the correct machine? This seems like a management nightmare.