Really sorry this happened to you.
The vote does not reflect many polls that consistently say men and women want separate facilities. It also does not reflect guidance, regulations and legislation.
I research toilet safety. To do so I look at lots of viewpoints and case studies. I have come across mumsnet threads about toilets on different social media platforms. They attract attention.
Unfortunately, there are some people that talk about transgressing boundaries in toilets and they are trying to find loopholes in which to get men into women’s toilets. If they can’t do that they are trying to alarm women by saying that everything has to go unisex. This won’t happen for all sorts of reasons, including economics, discrimination, legislation, health and safety guidance and building regs.
There are a few court cases that have gone through recently that back what you are saying. And common sense.
The way the cinema should sort this is that they should have another accessible toilet that is heavily monitored, leading on to a public space. A changing places toilet is great as they are few and far between so people will have very specific needs that should be prioritised. What would be even better is for them to have a larger ambulant toilet, even an accessible one (all with door and partition gaps) within single sex accommodation. Therefore independent people in wheelchairs could go straight into a toilet that caters for their needs within safer and more hygienic designs.
Radar keys were introduced as people use toilets for sex, drugs and vandalism - not just because people wanted to skip any queues. The problem with creating any large, mixed sex toilets is that the design has to be private. They are prone to misuse. Single sex toilet-washroom with toilet cubicles that have door and partitions gaps are safer and more hygienic.