I think that both modeling choices would make sense depending on which specific type of misogyny is the concern. For example, interruptions would seem likely to fit your model better, while asking a woman out in an inappropriate manner might be fit by the random group member model better.
Although I think that the group size is realistically going to be smaller than 100 in almost all cases, often far smaller, which would also lead to less skew.
Edit: although if instead of considering how many women experience >0 instances of (significant) misogyny, and instead consider how much misogyny on average each woman experiences, then it would go back to being heavily skewed by the proportion of genders in each group.
I think that both modeling choices would make sense depending on which specific type of misogyny is the concern. For example, interruptions would seem likely to fit your model better, while asking a woman out in an inappropriate manner might be fit by the random group member model better.
Although I think that the group size is realistically going to be smaller than 100 in almost all cases, often far smaller, which would also lead to less skew.
Edit: although if instead of considering how many women experience >0 instances of (significant) misogyny, and instead consider how much misogyny on average each woman experiences, then it would go back to being heavily skewed by the proportion of genders in each group.