Not necessarily. It would depend on the situation. First, right now, I know that the military will not make men and women share berthing spaces. Second, if they did, and it was during bootcamp, I'd still feel uncomfortable, and maybe moreso due to the men showering with me, but it would be because I was attracted to them, not that they might be attracted to me. And the embarassment from having my period would be a lot worse in front of men, who are most certainly not comfortable with women's periods, no matter what sexuality they are. If it were later on in my career, then I might be uncomfortable around some men, but not all. While in the Navy, I only had male roommates when I lived off base. I am actually more comfortable around men because there isn't as much drama.
I have changed in the same area as some of the guys I worked with. It really wasn't a big deal. In fact, there were some guys who were more upset about it than I was, because they were nervous that I would file a sexual harassment suit against them, eventhough I voluntarily changed in the area, because there really wasn't any other nearby place to change and I was the first female to ever work in that shop.
I'm not afraid of being raped or even sexually assaulted by other servicemembers, certainly not while on duty and/or in a group shower. I know I have recourse, there are tons of witnesses, and I know that they know that there are rules against it. If they try something in a berthing or a shower, there will most likely be at least one other person in there. And if men and women shared berthing, there is actually a good chance that the other men and even the women who might be there would come to the aid of the one being assaulted.
I am a staunch believer in what makes people most uncomfortable about seeing members of the opposite sex naked is actually the foreignness of the anatomy of the opposite sex, not the actual sexual attraction. Men and women are different physically. Heterosexuals and homosexuals of the same sex have all the same parts (barring some deformity or unfortunate event). Their bodies basically operate and react the same way.