Is it permissible for a girl who is engaged to a non-religious person to meet another religious suitor with the intention of marriage, and then break off her first engagement if there is mutual consent, or is it necessary to break off the first engagement before meeting the second suitor?

Firstly, engagement is merely a promise of marriage, and both parties have the right to annul it whenever they wish, especially if it becomes clear that the other party is unsuitable. There is no dislike in retracting from it if there is a benefit in doing so. However, if they retract without a valid reason, it is disliked due to breaking a promise, though not forbidden.

Secondly, if a second suitor proposes during the engagement period, there are two scenarios:

1. If the second suitor is aware of the first suitor's engagement: It is not permissible for him to propose to her, nor is it permissible for her to accept him, due to the prohibition of proposing to a Muslim woman who is already engaged to another Muslim. This would constitute aiding in sin.

2. If the second suitor is not aware of the first suitor's engagement: There is no harm in him proposing to her, nor is there any harm on her or her guardian in accepting him. The woman may accept the second suitor's proposal if she deems him more suitable for her, and then she annuls her engagement with the first suitor. It is not a condition to annul the first engagement before accepting the second. What is incumbent upon the woman is to choose the one with good character and religious commitment.