What is the Shariah ruling on Muslims being cured of their illnesses after visiting Christian shrines and being anointed with oil there?

A Muslim believes in all divine messages. As for what contemporary disbelievers profess, it is not a religion a Muslim believes in, because the law of the Prophet Muhammad, may Allah bless him and grant him peace, abrogated all previous laws. It became obligatory upon all people to believe in it and abandon whatever contradicts it, otherwise they will enter Hellfire.