Can a washing machine/dryer from other brands be installed in Ikea Metod?

Hello I believe you are operating under the wrong assumption that dryers/washing machines are built into cabinets like stoves or ovens. In fact, they are simply slid under the countertop and between the surrounding cabinets like a dishwasher/under-counter refrigerator. So if you want a door in front of it, it will be attached to one of the neighboring cabinets anyway. Since you make the fronts yourself, I also see no problem in making the doors a bit wider.

So if you want a door in front, it will be attached to one of the neighboring cabinets anyway.

At BSH, there are also fully integrated washing machines that have hinges for a cabinet door. This is probably not without problems - due to imbalance, such a machine can also shift slightly, which, of course, affects the gap dimensions.
Regards,
IKEA friend