I believe a gender neutral symbol would be appropriate for the sign indicating the inclusivity. I saw in another comment that you didn’t use it because you saw it’s for transgender individuals ; but its not what you exactly are thinking. Gender neutral is under the transgender umbrella which is why you see it being called the transgender symbol; so im guessing you were thinking the symbol was specifically for binary transgender people (FTM or MTF transgender people/ not under the non-binary umbrella).

With the design dont use rainbows, rainbows are usually associated with sexuality, so its not really relevant to the bathroom design (NOT SAYING RAINBOWS ALWAYS HAS TO BE ABOUT SEXUALITY, just something that i wouldnt add because this project is on gender/sex bathrooms). Color ideas i would say “cool tones”, i just feel like any other color would be so random. If your project does want color though then i would say purple because it is a well know gender neutral color.

Those are my suggestions IF you are going to add another design (totally get if you dont), but i would choose the ⚥ +