Genesis 1:27:
So God created mankind in his own image, in the image of God he created them male and female he created them.
FWIW I think this doctor is an ass. If a patient introduced herself to me as “Lady Jane Gray” or “Captain Kibble” I’d use that, regardless of what I privately thought. I might struggle to use the right pronouns, not out of intent, but because modifying language is hard. But I’d give it my best shot.
If you’re the patient’s psychiatrist then challenging them may be in your clinical remit. Otherwise? Address people how they want, because a medical consultation is about them, not you.