Should a young man annul his engagement to a girl whom his parents do not approve of due to her characteristics and behaviors conflicting with religious and social values, and would divorce in this case necessitate judicial decree and rights for the fiancée despite the contract not being Sharia-compliant?

The obligation to obey one's parents is a known principle in Islam. If the woman is ill-mannered and disregards lawful and unlawful matters (halal and haram), then the young man must leave her and obey his parents in this regard.

As for divorce, the pronouncement must occur if the marriage contract has been concluded. Her right, if the contract was finalized, is half of the agreed-upon dowry, as Allah Almighty says: "And if you divorce them before you have touched them and you have already specified for them an obligation [dowry] - then for them is half of what you specified, unless they forgo it or he in whose hand is the marriage contract forgoes it. And that you forgo it is closer to righteousness. And do not forget graciousness between you. Indeed, Allah, of what you do, is Seeing." (Al-Baqarah: 237). If a dowry was not agreed upon, then a compensatory gift (mut'ah) is determined by custom.