What is the ruling of Islamic law on the marriage of a paternal cousin to a Shiite man, and what are the ways to dissuade her from this marriage, especially since her father approves?

If the Shīʿa invoke ʿAlī, Al-Ḥasan, Al-Ḥusayn, and the like, then they are committing major shirk (polytheism) which expels one from the fold of Islam. Therefore, it is not permissible to marry them, nor to marry their women, nor is it lawful to eat their slaughtered animals, due to the Almighty’s saying: "And do not marry polytheistic women until they believe" (Qur’an 2:221), and "And do not marry [your women] to polytheistic men until they believe" (Qur’an 2:221). It is obligatory to advise relatives who insist on these marriages; otherwise, the matter must be referred to the Sharia court.