How is this synchronous AC gear motor being reversed?
A basic 2-wire synchronous motor will start randomly in either direction, or may fail to start at all.

Usually, cheap uni-directional motors, as used in clocks for instance, have a mechanical spring/cam arrangement that engages if the motor starts in the wrong direction, and flicks the armature into the other direction.

A synchronous motor may be built with a directional bias, perhaps shading rings over part of the pole face, but this increases power consumption when running. 

Another possibility that might allow the controller to start the motor in the direction of choice with just two wires could be a magnetic bias to hold the rotor in a quadrature position with power off, then the controller starts power with the appropriate phase. This is pure speculation on my part, I've never seen it described.

If the motor will start in either direction, I would expect the washing machine mechanics to be able to tolerate this. If it's not meant to start in either direction, then perhaps any starting mechanism has broken.