Being examined by female docs is triggering for me, so I always have a male GYN. But I also get pretty freaked when a female observer is in the room. What a mess.
I started having GYN exams again after a long hiatus. I always arrange to have male practitioners. Once, my male GP did the exam. Then, I had a male GYN doc, didn't like him very much, and switched to my current (male) GYN. I also had to have some ultrasounds done, so I requested a male tech. Chaperone requirements have been all over the map.
My GP wanted a nurse in the room, but when he saw how I was, he agreed to do the exam without her. We had a longstanding relationship, though.
The first GYN had a female nurse with him. I was very disturbed, but I couldn't request that she stay out because I didn't know this doctor well enough to speak up for myself. I sort of went mute on the subject.
The second (and current) GYN has, by my request, arranged to have a male nurse present whenever I have an appointment. (Once, the male nurse was unavailable, and once he could not be there for a semi-emergency.)
The ultrasound tech had a form for me to sign to waive the chaperone.
I always specify my needs up front and see what can be done for me. My phobia has gotten rather worse since that first GYN appointment; I disassociated once and nearly passed out the second time. Yeah, I got me a few hang-ups. The bottom line is that you have the right to ask for what you need. You might not always be accommodated, but do ask well in advance. And if you simply prefer a female doc, you should be able to switch to one.