Is it permissible to shave the beard due to the parents' fear of the authorities, and is this fear considered a legitimate excuse for that?

Shaving the beard is forbidden except in cases of dire necessity. The mere apprehension of one's parents does not justify shaving it, unless there is a strong presumption of harm occurring, or if it is certain to occur. In such a case, there is no harm in taking the concession to shave it due to necessity.