Her curiosity is totally natural... she has just found out that boys have different "equipment" than girls do. (We started out with 3 girls... one day, we were swimming at a friend's house.. they had a boy about 2 years younger than she was at the time.. I think she was about 4, maybe? Anyway, when they came inside, the other mother had taken the boy's swimsuit off, and was wrapping him in a towel... my daughter said, "Johnny has a funny bottom down there!" She had never seen a little boy's privates before! We just said, "yes, Johnny is a boy, and little boys are different than little girls.")
Yes, her behavior can be embarrassing....
The best way to handle this would be to remind her that, just as the class explained that we don't allow other people to touch or view our privates (except a doctor, etc.), it is not right to ask to see someone else's privates.
Just remind her when she goes to school each day, that she isn't supposed to ask anyone to see their privates. Don't do it in a "shaming" way, just matter of fact... "Remember, Sally, we don't ask other people to see their privates..... their privates are just for them." Just do this as a daily reminder, and eventually, she will probably start saying "Yes, M... I know!"
Also... talk to the teachers at school and let them know how you are handling it, and ask them for any other suggestions. That also shows that you aren't just "blowing it off" and not taking it seriously.