Not to mention that it's well known, well evidenced fact that in mixed sex situations men dominate and women do not respond in the same way as they do in a single sex situation. There's a few different groups I regularly attend and sometimes they are women only, and sometimes a few men attend, usually friends or partners of the women members. When it's women only, a lot of the women talk, offer ideas, state opinions, discuss with each other. When men are present, even if only one or two men in the group, they dominate the floor, they interact directly with the presenter if there is one, they ask most of the questions, and the women who would usually talk? Say very little and some don't participate at all. These are nice, normal men.
Women want times and spaces that are about them, their interests, their bodies, their competition, their own excellence. We need to stop worrying about is there sufficient hard peer reviewed evidence to dare to think about saying 'no' to a man and think instead about why as a society we don't see women as equally human to men and entitled to the same respect and autonomy. Why we seriously still view women as resources with an inbuilt birthright to put the wishes and needs of men ahead of themselves.
And why we're seeing women in this awful way while pretending to believe that some men turn into women. But not real women: not a the kind of women that come without needs or feelings, and have a duty to be a codependent doormat.