Now Mentats make perfect sense for doing political and other projections for the great houses but it would be impossible for a Mentat to replace the everyday control systems.
The little microcontroller in the air conditioners for example is a computer by definition, and if such microcontrollers don't exist then how does society function as a whole?
Computers on their own don't do anything (other than heat up the room); they're only useful when running a program (e.g. a control system, or whatever).
If we have a computer running some program, it can always be replaced by a dedicated circuit for performing the same calculations, known as an ASIC (Application-Specific Integrated Circuit). ASICs can be vastly more efficient than computers (that's why they're used for bitcoin mining).
The main reason we use computers is they can be reprogrammed: existing machines can be used for new tasks, and updates/fixes can be made to the program without having to build a new physical machine/circuit/whatever.
There's also nothing particularly special about electronic circuits, other than their speed. Both computers and application-specific machines can be built using clockwork, billiard balls, etc.
Hence the main effect of forbidding general-purpose computers would be slowing down innovation: they wouldn't have the quick feedback cycles we enjoy when hacking on software; they'd need to disassemble and rearrange their wiring/gears/etc. every time; and new products can't be 'downloaded', they'd need to either be physically shipped, or built on-site from blueprints.
This also incentivises simplicity (which is good if we also want to avoid "borderline" thinking machines), and solving problems using clever tricks/hacks if possible. This seems to fit well with the Dune universe: lots of their technology is simple, ingenious, and pretty much unchanged for thousands of years (e.g. shigawire, stillsuits/tents, all the various uses of suspensors like shields and glowglobes, etc.).