Some of us remember the coed bathroom featured on the hit 90s show Ally McBeal. It seemed like a progressive but not so far fetched idea at the time. So WTF are we doing still arguing about this 25 years later? These bathroom nazis need to get a grip.
The real answer. Skip the whole gender thing if it's an issue. Certainly public restrooms being ungendered entirely won't be a problem, who knows why we have it this way...
The answer is sexism. When women started to enter the workforce there was concern that they would get "overwhelmed", so gendered bathrooms were created to give them a space they could go to that feels like the home.
No, bathrooms are a fairly modern invention that evolved from outhouses, which are gender neutral, or chamberpots, which are generally made specifically for one person. The invention of the modern bathroom with indoor plumbing came about in large, male only factories, and then a new environment, the restaraunt.