Whatever sex they were, whatever size speculum they were using they should not have continued a procedure on someone who was screaming and crying.
In hindsight, I agree with you, they should have stopped and offered a lidocaine shot. I know that now because I've had anaesthesia-assisted coil fittings and know that I have a choice other than "put up with agony or have no coil". At the time I thought it was a choice of agony for a few minutes or pain every month for a week (I was getting a Mirena for endometriosis) and pregnancy risk.
That's not the point of the thread though, is it?
The point of the thread is that women have the right to request a female HCP for any reason and have that request granted unless doing so is impossible.
The lovely male gyn is a research professor who has spent his career improving women's options for endometriosis, menorrhagia, and dysmenorrhea. Literally, his life's work is to make our lives better. If I there's ever a man I can trust with my cervix, it's him, and at a logical, forebrain level I try to. Knowing his dedication to women's health didn't stop my hindbrain from registering him as male and reacting accordingly.
Trauma responses aren't under voluntary control and we shouldn't be castigated for having them.