So coincidence that even replacing with a new AFCI breaker, the washer still tripped the breaker. So the homeowner had the appliance store replace the board in the washer and it still tripped. Then the appliance store just gave them some brand new SAMSUNG washer and dryer set. No issues.
What do you suggest then?
I would suggest that all appliances\electronic devices sold in the US have to meet a stringent set of EMC standards. This would include the AFCI devices! That is the best possibility of having them all place nicely together.
In order to sell equipment in Europe manufacturers need to CE mark their equipment. That requires them to test against a wide range of EMC standards. This is done to minimize electronic interference with each other.
Assume that the AFCI in question is tripping due to the fast transients generated by relay switching. That type of electronic "noise" can be readily simulated and tested for. When standards agree on the allowable amount of noise that one device can emit, all others must then be tested to assure they will not be susceptible to erratic behavior when subjected to that same level ( in practice a greater value by some margin) of "noise or interference".
It is possible and likely that the Samsung equipment is CE marked. I doubt the AFCI is.
It is also very possible that the addition of an integral EMI filter to the Whirlpool would allow it to work with the AFCI.
I do not believe you can blame one more than the other without them both being held to the same set of standards. That being said, AFCI's were introduced way before they were ready for prime time and have a ways to go yet. Perhaps if they cost $200 each rather than $40 they could be made to place nicely with everybody else.