First, either you are a male or you aren't. I don't understand the "identify as a male nurse".
I was 1 of 10 males in my nursing program. In my opinion they want more male nurses because patients are getting heavier. I do notice that the male nurses are called for everything: getting a patient up, turning, transporting, unruly patient, etc. There are some meme's out there that while they are funny they are also pretty accurate.
I believe men were discouraged from going into nursing because for the longest time if you were a male and you went into nursing you were considered, how do I say it gently, "not masculine". In my experience that seems to be the complete opposite. I will say though Ive never been asked "why not become a doctor?" but I have been asked a-lot if I plan on becoming a NP (which I do not).
Regarding OB, Im 100% fine with not being given the same access that female nurses are awarded. I told my OB rotation instructor I am here to get my C so I can move on. When I did have a female OB patient that allowed care I had a female nursing student or the instructor with me at all times, especially in the times we live in today.
Does being a male hinder their career? I don't think it does. If anything I think it accelerates it. Let's be honest, male nurses are treated differently than female nurses. I heard it all the time from my female co-workers. Some doctors talked to and treated male nurses better than female nurses.
I think men in nursing will continue to grow but I don't think it will ever be a male dominated field like physicians (although there continue to be more women in medicine, which is a good thing).