If these tidal forces naturally cause synchronous rotation for each object, why is the Moon currently in synchronous rotation with the Earth, but the Earth is not in synchronous rotation with the Moon?

Tidal locking in the most well-known case, occurs when an orbiting astronomical body always has the same face toward the object it is orbiting. This is known as synchronous rotation: the tidally locked body takes just as ... if a giant planet perturbs the object. Not every case of tidal locking involves synchronous rotation.