The latter removes any scope for taking circumstances/details into account which is an issue irrespective of gender/age etc (e.g. "believe men" or "believe children" would be equally absurd).
But you just said "believe women" is fine whereas "believe men" or "believe children" is absurd. I don't follow the distinction you're drawing here. They're grammatically equal.
I was falsely accused of sexual harassment when I was in 1st grade. I didn't start having anything resembling attraction to women until 3rd grade, by the way.
We had some sort of combined activity with some 6th grade students. I dropped my pencil and crawled under the table to get it, and got back to work and didn't think anything of it. A 6th grade girl at the table got up and left the classroom, and 15 minutes later I was called up to the principal's office. They told me I was in big trouble for looking up girls' skirts and if I had anything to say for myself. I just got really confused and started crying, I told them I had no idea what they were talking about. Fortunately they believed me, but the fact that they took things that far in the first place left a very bad impression on me regarding both school administrators and sexual harassment claims.
Edit: this was in the early 90's, by the way. I'm sure it's only gotten worse.
