To refer to a long running debate on mumsnet.
Some people do not want to get changed in the company of opposite sex 'tweens'. Many parents don't want their over 8 children to get changed without adult supervision. The compromise is mixed changing and single sex changing areas.
This isn't always possible, so the debate runs on. However, that doesn't mean that the different groups deny each others' existence or don't understand the other point of view.
Take out the ideology and the need for affirmation, and it isn't difficult to find common ground.