I'm going to have to say that in all likelihood traumatised women have probably declined inpatient care because of mixed sex accommodation and died as a result. A large proportion of seriously mentally unwell/suicidal women are survivors of sexual and/or physical violence and are scared of men. And it's not uncommon for those who die from suicide to have presented at emergency care or to have been previous inpatients.
I've had the much less difficult experience of going to a mixed "psychoeducation" NHS group. And seeing why women self exclude from mixed groups, here a requirement to being offered therapy. A man, openly on various illegal drugs and agitated, was physically aggressive and verbally abusive to me in this "education group". I had to leave and was quite scared, unusual for me. The staff didn't intervene.
I raised it the next week and asked why they did not interfere and the staff told me "it was a good experience for me" .WTF. I told them I had plenty of experience dealing with aggression and more was not going to improve my mental health! A lot of women didn't return for the second session, I presume they didn't feel safe...but if it cuts down demand for therapy so who cares...I only returned because I correctly predicted this man, having had someone stand up to them, wouldn't return...
Sorry for the long post, but I'm really grateful this broader issue has gotten into the news.