We have unisex toilets at work - smallish staff team, more women than men. Two cubicles within one room, sanitary bin in both, sink outside the cubicles. It really has never been an issue.
Not many people I know would clean a moon cup in a communal sink anyway, regardless of it being mixed or women only. Not sure other women really want that happening in the sink just in front of them either tbh. Besides - don't you then have to go back into the cubicle to reinsert it? Just wipe out or carry a small bottle of water for rinsing in the cubicle.
The toilets remain clean, tidy and non smelly. Our make staff are perfectly capable of aiming it would seem. Mind you, we don't have that at home with dh, nor any of the male guests who visit. They seem perfectly able to aim directly!
We have staff of different religions - not been an issue for them either.
There is also a disabled toilet available though this is available to anyone to use, male or female, disabled or not. We don't currently have any disabled staff or pupils, but it is there for people to use should they need that facility, in additional to all staff the rest of the time.
Our EYFS toilets and some of our Y2 toilets are newly refurbished and are also unisex. The older KS1 toilets will be refurbished in time and will probably be unisex too. I am pretty sure the toilets in the KS2 school nearby are all unisex as well. Although there were some concerns initially it would appear, 2 months later, the initial worries have proved unfounded, for now at least.