But in health care, the patients needs come first above the doctor's personal sensibilities or feelings (which you refuse to accept).
The trans identified male doctor already knows he is a male with a trans identity (obviously), so he should exclude based on that given the patients wishes.
The onus is not, and should not be on the patient to narrow focus her request that any same sex intimate care she receives excludes 1) male doctors and 2) that little subset (numbers wise) of the male sex that have some unprovable (for the moment) feeling that they are women - even though their sexed bodies, the law, and reality prove they are male, and the perception of the female patient is that this doctor is a trans identifying male.
In a professional sense it would be ethically wrong of the trans identified male doctor to even present themselves in that situation in the first place, even if he then removed himself after the patient repeated her request with the euphemism "I'd like a different doctor please". Even worse if he were to carry out the intimate health care procedure if the patient didn't say anything, silence is not consent.
In a moral sense it would be wrong for the trans identified male doctor to present themselves in that situation, putting the onus on a patient who may be too stressed, sick, unconscious, traumatised at having a male bodied person present themselves for intimate care, etc.
I'd also like to forestall any attempt to tell me that the patient might not notice, or know that the doctor in the scenario presented was a trans identifying male, because that would actually make it worse.
In the eyes of the law it would be a criminal offence if the trans identified male doctor in that situation carried out that intimate health care procedure.
ETA: Changed "it" to the bolded & underlined "they are male" to clear up any confusion