Just to clarify a couple of misconceptions here - and of course, I am not speaking for all the women who have difficulty with a male MW or delivering obstetrician:
It is not a rational "ooh, that bloke must have something wrong with him to want that job." I've worked in care for years with many fantastic male carers, I'm well aware that many are capable.
It's not being bashful about my fanjo - no bother with male doctors conducting smears etc.
It is not as simple as that.
In labour, and just before it while being induced, I found everything very triggering. What was triggered was a panic reaction. I am normally very controlled and assertive. I was unable to be so in that situation.
It is not fair or reasonable to expect all women to cope with a male presence during what can be a very traumatic time. And currently, you are expected to, because of course, the Almighty Doctor cannot be contradicted. I'm glad you can request a different MW, but it is far more difficult to get a different doctor.
It is not fair or reasonable to expect a woman to explain herself.
To do so is to place the feelings of the male professional above those of the labouring woman. That is not right.
Pregnancy and birth are unique to women. There is no comparable experience. For example, you could compare a smear to a prostate exam. But labour and birth is different, it's not an illness, nor is it a routine check.
I appreciate I'm in the minority, most of MN are very right-on regarding this issue. I would suggest this is one instance where "equal" does not mean "exactly the same."
I imagine this sort of thing is covered in the training of MW, male or female. It certainly should be, as the percentage of women who are either abuse or attack survivors is very high, and they will be the women who need kindness and support, not accusations of sexism.