Chantal,
I play safe and use disabled facilities, OK you could rename them gender neutral as they are intended for either gender. On one occasion it was out of use, so I stood pondering for a moment when a GG from my social group grabbed me by the arm and dragged me into the Ladies , all she said was you look so convincing no one will notice . There were other women in there so I just smiled and found a cubicle, when I'd finished the wash area was empty so I washed my hands found my hairbrush in my bag and was just retouching my lipstick when another woman walked in, she looked and said nice colour before disappearing into a stall.