I see where you're coming from, KeenReader, but the way it is phrased originally makes it sound like no one, including the father, is allowed to bring this subject up with the mother. It's true that it is rude for friends, grandparents-to-be and other relatives to invite themselves into the delivery room, but I think this is a perfectly reasonable discussion for new parents to have.
And as for who has final veto power between the mother and father, that probably varies from rel@tionship to rel@tionship. I'm not sure that's really an etiquette issue. At least not one we will ever reach a consensus on. 
I think that they can ask, but the mother does and should have final veto power.
Let's face it, childbirth is a procedure that involves pain and can in many ways involves what can feel to the mother like a major lack of dignity. She should not be made to feel guilty or told how "hurt" others are that she doesn't want them there while she's undergoing a painful procedure that involves pushing something out of the lower end of her body or having an incision made in her abdomen and something removed-even if it's a child.
I think we need to clarify - are we talking in the delivery room? Yes, mom should of course get final say. At the hospital in some other area politely waiting for parents' cues? I think that should be joint decision. Grandparents or whoever else is allowed to be at the hospital can see the new baby through the window in the nursery shortly after birth (at every birth I've been to) with no disruption or interaction with the new mom if she so chooses.
I'm talking about at the actual delivery. I agree that who comes to visit in the hospital afterwards should be a joint decision between the parents.
Sorry, again I mean at the hospital in the waiting room while the mom is in labor/delivering vs. in the delivery room itself. Not visiting afterward. Mom should be able to veto delivery room, both parents should be able to decide who is in the waiting room while mom is in labor. My comment about seeing the baby in the nursery was shortly after the baby is delivered, for people who are waiting for it to happen. You can do this without even going into the new mom's room and she won't be disturbed.
A lot of hospitals are getting away with having nurseries now - there's a lot of emphasis on skin-to-skin contact with mom and keeping mom and baby together after delivery. When I had munchkin, there's absolutely no nursery at our hospital, just a tiny room where they bathe/weigh baby, then bring him or her back to mom. Additionally, our hospital strongly recommended not having family wait in the waiting room - the nurse manager said quite a few times pushy family members steamrolled over a tired mother after the birth.
In my case, my parents were at the hospital as our supports and I refused to agree to DH's mother coming (she's now cut off due to toxicity), but in the end, it didn't matter - the only ones to see Munchkin's birth was my OB, a pediatrician and a bunch of nurses. I had a c-section and had to be put under because a spinal wouldn't work; Munchkin was given to his father with strict instructions from me to the nurse before I was put under that no one, not even my own mother, was to hold Munchkin except his father, until I did. Getting over the guilt over not being there for his birth was immense - if other extended family members had been gawking through a window at him, before I'd even seen him, the hurt would've been even worse in my post-partum mind.
