AFCI Trips When Stainless Steel Hoses Touch Washing Machine Cabinet. Why?
Many new washing machines have inverter drives on then now, and those inverters create what's called "Common Mode Noise", electrical noise referenced to ground. The washer doesn't need to be running, just plugged in for the inverter to create CM noise. 

I'd say that your ground connection to the outlet or in the machine is loose or missing, so the CM noise is discharging through the machine frame itself when it comes in contact with your plumbing. Think of it as if it were a static charge built up from walking on nylon carpet and you touch a metal surface. That discharge looks like an arc fault to the breaker.

Check that inside of your washer, the bonding jumper is connected. it will be a green wire going from the machine frame to the ground terminal that the cord is connected to. If that's OK, get a receptacle tester to make sure your receptacle is connected to ground.