You are very naive to believe this won't happen in most of the western world.
Currently with feminism all the rage, and sue happy people all the rage, there are lots of good reasons to avoid getting sued.
For example, I know a couple of taxi drivers that refuse to drive women, specially a single woman, because of repeated problems with false rape accusations. (likewise, there are lots of real rape cases with taxi drivers involved).
EDIT: I remembered when my dad worked at a church helping people, and kicked out of his office any women that asked him to lock the door, no matter the reason. Then he explained to me he has a personal rule of never locking himself alone with a woman in a room, unless it is my mom.
Currently with feminism all the rage, and sue happy people all the rage, there are lots of good reasons to avoid getting sued.
Don't blame "feminism" for that. False rape/harassment accusations occur and it's very wrong that they do, but they're not a product of feminism.
False rape/harassment accusations are the antithesis of feminism. First of all, that game is old as empire: women using social power and implicit credibility to get other men to use violence or bring social harm on men who displease them. It happened in the antebellum South, which is not exactly known for being a stronghold of feminism. It has probably existed in every society.
Women have a certain social power-- the ability to make men fight over them, to defend their honor, et cetera-- that is decidedly unfeminist in origin. Whether they choose to use it comes down to the individual. If anything, a feminist should be less likely to use that, instead preferring to solve her own problems instead of calling in a man to rough someone up.
Feminism and bad female behavior shouldn't be linked together. Bad behavior is as old as dirt on all sides of any class, gender, or race divide, and it's irrelevant to the real debate. At any rate, feminism is about equality, and abuse of archaic, gendered social powers goes directly against that purpose.
You are partly correct, but feminism brought lots of social changes that affect this.
Also, lots of feminists defend female supremacy and they are very clear on that (most infamously, Valerie Solanas).
I mentioned feminism in particular, because after its rise, rape is a crime that shifted from being almost never prosecuted to be kinda over prosecuted, with cases that involve strangers the "innocent until proven guilty" being thrown away from the window. (while sadly, rape by known people, that is still the majority of the rapes, is still mostly not prosecuted properly).
Unfortunately I don't have time now to grab the exact statistics and research, but there is some evidence that courts tend to be biased toward women, with many avoiding punishing false rape accusations (even when the accused life is destroyed).
Mass panic and mass hysteria always happened in history, feminism changed the subject of the panic and hysteria, not the frequency.
In London in a year there was 214 reported cases of sexual assault by women that got into a unlicensed cab, and 54 rapes in unlicensed cabs (I did not found stuff about licensed cabs, the location I saw this was specifically talking about the unlicensed ones).
Of course, how much of this is real assaults or fake accusations, is not stated either.