Firstly, we are dealing with someone whose family has told her that she will go to hell for daring to believe that she is anything other than a heterosexual cisgendered male. They are the ones trying to get her to see the priest. I think that it is a fair bet that he will share their bigotry.
Secondly, no decent therapist will "have a final say in whether one is transgendered or not" but they (unlike the priest) are trained to empower the patient to work it out for themselves. The priest with (according to you) similar training will have been schooled in how to persuade his parishoner to toe the church's official line not in how to empower the parishioner to discover for his/her self.
I have no problem with anyone who wants to believe that another person is the authorised oracle for their chosen god and who goes to that person to seek the authorised answer to a religious dilemma. I do have a problem with someone being sent by people with closed minds to a person "in authority" to be persuaded of something about which that authority has no understanding.