I don't think I'd have a problem with it but I guess I wouldn't know until it happened. Lots of women report feeling much more vulnerable in pregnancy so might feel differently.
I've supported lots of women who for very good reason will only see female HCPs unless it was a dire emergency. Given what they have previously been through, no-one has ever questioned their right to be examined/treated by a woman but sometimes they have had to wait longer for appointments/to be seen.
Personally, I've always had very good male HCPs. My favourite GP is a man and I've had amazing care and understanding from him and trust him implicitly.
I've had to have some fairly intimate examinations and felt as comfortable as I could have been in that situation. I've also had emergency surgery and almost everyone in the room before I went to sleep was male. I don't remember giving any shits, I'd have been terrified no matter who was in the room.
So whilst I don't have an issue, I absolutely support the right of women to object.
It does really piss me off when people question the motivation of men who go into certain professions.
It's not just HCPs but teachers, nursery staff, nannies, social workers etc
There are bad people everywhere, some people will try to use their jobs or volunteer roles to gain access to certain groups of people and do harm but these are the exception and the solution is not to stop men from becoming midwives or primary school teachers but I've heard a lot of people argue that we should.