miritchka – I am surprised to hear you say that. Do you know how many women don’t go into labor long enough to get to the hospital? Why would you call it irresponsible? Many of my labors started with heavy labor 5 minutes apart and rushing to the hospital still only gave me 10 minutes. I have several friends who had the same thing happen who delivered in street clothes or at home. It is not about responsibility and it is not something to be embarrassed about. A short labor is a bracha, not a busha.
The time I got to the hospital before my doctor I had a whole group of people rushing in to check on me (instead of the normal one or two) and I found it very uncomfortable. People have very different sensitivity levels toward tznius.
Like Gamanit said, in time of medical need it is more important to get care from whomever can deliver it, but in non-life threatening situations I certainly would prefer a woman. I don’t think it in ANY way to be pritzus, I just find it extremely uncomfortable.