Washing machine pressure switches directly control the hot and cold water inlet solenoids and so are rated for quite high currents - 15A at 230V AC is typical. So for low-voltage DC applications, the switches can certainly cope with (say) 5A. This means that, for most loads, a relay won't be needed.
Excessive force can result in centrifugal stresses that could cause the appliance to move or walk across the floor. Most automatic washers are equipped with an off-balance or out-of-balance switch that stops the washer from spinning and causes a buzzing sound at any point in the cycle when an off-balance condition occurs. On some of the appliances, the master timer knob switch was in series with a single-pole double solenoid.