Tough Guy no. 1265 wrote

I have a digital plug in timer which says on the back,
"Not suitable for dishwashers and washing machines".
The only reason I can think of is the inductance of the motor.

It might be because they are usually programmable and don't
necessarily work properly if you try to turn them on using a
timer in the sense that they won't necessarily have kept the
program you have programmed.

But it's rated at 3.2kW, and it uses a relay (I can hear it). So why?

It may be rated for the motor current if its that.