Must I obey my mother and call off my engagement to a religious and well-mannered girl due to her unjustified rejection, or should I continue the engagement and displease my mother, knowing that I do not want to wrong the girl and that my mother's رضا [رضا: approval/contentment] is important?

If you are harmed by leaving the girl you wish to marry, then you are not obliged to obey your mother in dissolving the engagement. Try to persuade her by seeking the help of someone who influences her. However, if you are not harmed, then there is no blame upon you for dissolving the engagement to please your mother. You must honor your mother, treat her kindly, and never mistreat her under any circumstances.