i doubt women would want their daughters aged 5-10 to disappear into a dirty mens loo - why let your sons?
Err...because they are male and their DDs are not...
If they are next to each other surely if the mens are dirty the womens are too 
some children do not speak out when approached
I think the answer to this is that you teach them to speak out loudly if approached, you don't take the assumption that you can't let them in a loo.
I was a very shy DC but I embarrassed my mother when I was 3 yrs old (she was pleased really). A man tried to help her onto a bus by taking me (he was just being helpful-nothing more) and apparently I said 'put me down, put me down this minute'! No one even taught me that.
I'm sure that you can tell DC there are times that you can shout at an adult.
It is however very rare. You are going to have to do something-they will have to go into the gents eventually and they will have to go places without mother eventually. Otherwise they end up like the poor 17yr old on the helicoptering parent thread who thinks they can never live without their parents because they have no idea how to cope with normal people and normal life-they have been so protected.
I think seeker has said at least 3 times it isn't about the attitude of women.
It is about the poor DS.
People make it seem as if it is the norm for boys to go into the ladies, I don't think that it is. From motorway service stations, shopping centres, museums,zoos, parks, pubs, cafes etc etc I visit the ladies and I never see boys above about 6 yrs in with their mums. The only exceptions are SN, and that is completely understandable.
Those of you who don't like it-why not practice in somewhere like a motorway service station first-I would say they are completely safe-so many men are in and out-they are never empty and no one would risk it (and if they did- a quick shout of 'get off me' and a kick in the shins would get help from some quarter).