I have not yet received the AF120 but I did a little more troubleshooting inside the Kenmore washer. The linecord comes into the washer and goes directly to a line filter. Unfortunately, the line filter that Kenmore selected has both the input and output wiring on the same end of the filter. This allows the line filter to be "short-circuited" by the noise it is trying to filter out. In other words, the filtered lines and unfiltered lines are so close that the noise couples from input to output thereby bypassing the filter. I added a ferrite to the input lines of the filter. The ferrite was snapped around the phase, neutral, and ground lines right at the line filter. I moved the output phase and neutral wires as far away from the input wires as was possible. This appears to have solved the problem. We have washed at least 6 loads of clothes and the X10 lights have not come on. Previously, the lights would come on every time we washed a load of clothes. I'll keep the AF120 filter for the next appliance that causes problems.
Ferrite p/n: Fair-Rite 0443164151