Should a young man abandon his fiancée, despite her being of good character and religious commitment, because his parents reject her without a convincing reason, or should he proceed with the engagement?

If it is only an engagement, then you must obey your father if he orders you to leave this woman, while trying to convince him to complete the marriage with her if there is no valid reason to leave her and she is religious and of good character. However, if your father did not order you to leave her, but rather left you the choice, then you are not obliged to leave her.