Do you have any more examples other than the freemasons? I had assumed we were done with needless segregation (excluding bathrooms and such).
The only thing that makes sense in my mind is that male dominated spaces have non-explicit social barriers in place that are being approximated by the explicit barrier the museum has set up.
In the UK there’s golf clubs that have pretty toxic atmospheres and dress codes but aren’t legally allowed to bar women.
Sorry if this is super ignorant, I’m acknowledging the problem I just want to understand it better