What is the ruling of Islamic law regarding a fiancée's insistence on adding non-mahram men on Facebook, despite her fiancé's refusal and his presentation of fatwas that prohibit such actions, and is the fiancé entitled to annul the engagement because of this?

A girl's participation in social media is permissible if it is within a public forum that everyone can access. What is forbidden is private communication, because it is a means to discord and corruption. The most important thing to consider when choosing a wife is her religiosity and character, for the Prophet, peace and blessings be upon him, said: "A woman is married for four reasons: for her wealth, for her lineage, for her beauty, and for her religiosity. So, choose the religious one, and you will prosper." If the girl is religious and of good character, then there is no harm in completing the marriage. However, if she has weakness in religiosity or a defect in character, then it is better to annul the engagement, because it is easier than divorce after marriage. Annulment of an engagement is permissible when necessary and disliked otherwise.