His client is a seriously disturbed woman, actually, and a Christian institution has the duty not to encourage her illness but to help heal it. That is, by getting Christian counseling for her, or by refusing to continue employing her to make her realize how seriously this is taken.
Humoring this delusion will not help her.
I have been particularly convinced of this since reading about that poor woman in the Netherlands who "became" a man and was still miserable - in fact, more miserable - and had herself euthanized. She said her parents hated having a girl, treated her badly (to the point of child abuse, IMO), and made her hate herself all of her life. But "changing genders," which of course is impossible, didn't help either because she was still miserable and now a complete freak.
Christians need to stand against this while at the same time reaching out helping arms.
A religious school should not be compassionate to such a one by keeping her teaching their charges. “Compassion,” as in keeping her on the job, would be something very different for her students. False compassion for one sinner that contributes to the damnation of many others is kind of questionable, I think.