Does falling into apostasy—Allah forbid—because of this study necessitate abandoning it to preserve one's religion, and how can the family be convinced of that?

Apostasy does not occur merely by studying poetry that contains apostasy, unless the student believes in its content. The obligation to cease studying in schools that include such material stems from the student's fear for their religion. If they fear straying, then it is obligatory to distance themselves from it, and obedience to parents in disobeying Allah is not permissible. However, if the student possesses sufficient knowledge to distinguish truth from falsehood, then there is no harm in it, for the predecessors studied pre-Islamic poetry despite its containing some false beliefs.