A tract of modest houses near here were built about 1968 by the same builder. No-hub cast iron drains. The washer box is in the wall with 1 1/2" drain and concealed below it is an extremely deep cast iron trap with sharp bend at the bottom. It is not unusual for the washer to discharge water faster than the trap can handle it with the resulting minor overflow at the box. Even a 1/4 snake will not go through the trap due to the sharp bend at the bottom. Replacing with PVC seems to the best solution.