“Unisex” actually implies “gender neutral”, or “single/one sex”, meaning there is no differentialtion between sexes” and is usually used to describe clothing or other articles that may have previously been assigned to a specific sex. This term also has sometimes been applied to bathrooms in areas where the term “unisex” is in wider use.

Lastly, there are some places that simply put both genders side by side, as in “Male/Female toilet”. And I once saw a sign saying “Any-sex” toilet.

Therefore there may be an opening for a new word if you’d like to coin one, as I have yet to hear a word that singularly meets the precise definition you sought in your question, while lacking any connection (current or previous) to “education.”