Commiserations to anyone who suffers from endometriosis, because it sounds a truly debilitating condition.
Of course it doesn't follow that a male gynaecologist would be any less sympathetic to women than maybe a female one would be. Slightly side stepping this particular ailment, I did a while ago read about women who had had vaginal mesh inserted, and in great pain as a result but having their concerns dismissed and treated in quite a sexist, misogynistic way by male doctors, suggesting what they were suffering was psychological and not physical. Given the complexity of many gynaecological conditions that will affect only women, the one thing I imagine most women want, is to feel comfortable with their doctor who will empathise and not patronise by treating them as a highly strung hysteric.
I did read that the CEO of a Prostate Cancer charity was a woman, I'm not sure men per se feel as threatened as women do in this current climate, for example would they, men, be described as "people with prostates"? I just don't see indignation coming from men, for numerous reasons, mostly they wouldn't feel threatened by trans men entering what would be a private space, if trans men entered a male sporting event, no doubt they'd be thrashed and possibly they don't feel language is erasing their status as men.