Am I allowed to do Mut’ah with a woman who says she believes in a higher power but does not identify as Jewish, Christian, or Muslim?
Bismihi ta'ala
Temporary marriage can only be performed with a woman who is from Ahlul Kitab, i.e. she is either a Muslim, a Christian or a Jew.
If she is of any other faith, or just believes in a supreme being, but does not follow any of the 3 Abrahamic religions, then you cannot do mut'ah with her.
And Allah knows best.