If failing to believe unconditionally in a male's chosen gender identity and not treating them in every way, exactly as if they were the sex they'd choose to be (regardless of the barriers/issues/trauma etc for you) is transphobic....
I'm afraid doing so is gynephobic.
You can either do what the male person feels they need, or what the female person feels they need. In this equation, you're putting one person of the two under the bus.
If it's the male person - they may feel upset, rejected, not validated in their gender, and this may be very distressing for them.
If it's the female person - they may be unable to access health care, accept necessary treatment, and possibly die through lack of it.
Either you have to prioritise one and justify it, or you have to come up with a third solution. Like specifying, people can ask for a specific same sex hcp if they need one, and everyone accepting this is in the best interests of that particular patient.