grim
Forgive the physics lesson but it is relevant.
Despite common understanding, the original Schrödinger's Cat thought experiment had an unquantified probability involved, so there is not a 50/50 chance the cat is alive or dead. Also, the point of the thought experiment is NOT that there's no way to know whether the cat is alive or dead without opening the box (though it's correct). The real point of the thought experiment is this: because the release of poison relies on a Quantum event the cat is actually, very literally, both dead and alive at the same time. Opening the box forces reality to shift from the Quantum world to the Classical world and makes the Universe decide the cat's fate. Scientific experiments have proved that, in simplified version of this, the experiment holds true.
Now, grim, this is the important bit. In real world experiments, the likelyhood of finding a "dead cat" is entirely dependent upon the probability of the deadly random event taking place. Whilst the principle holds for any probability between 1 and 0, in the real world we only care when the probability is of a value that impacts upon us. Schrödinger's Pet Shop with a probability of deadly radioactive decay of 1 event per cat per hour will go out of business. 1 event every million years will do fine.
So, whilst you are logically correct, in the real world it doesn't make sense to treat terrorists and rapists as equivalent. The probability of any particular woman being raped is high enough for it to be a genuine concern, the probability of any particular person being blown up by a terrorist is almost zero. The woman's fear of rape is rational, the Islamophobe's fear of terrorism is completely out of proportion to the risk.
As for comparison with racism and ethical equivalence... the comparison you're looking for is this:
In America, is it wise for a young black man to consider the possibility that a white cop in a black neighbourhood will mistake him for a criminal and shoot him?
Does answering "yes" mean he's a racist? Possibly. Does being racist against white cops increase the young man's chance of getting home at night safely? Yes, because some white cops are also racists. So, who's racism is the real problem here, that of the young black man trying to get home or that of the cop with the gun looking for someone to shoot? And can we fix the white cop's racism by stopping black kids being afraid of him? Or does it make more sense to stop white cops shooting innocent black kids?
So it is with Schrödinger's Rapist. If women are sexist against men, it's because men are sexist against women and will act on that sexism to commit acts of violence against them. The only way to tackle women's mistrust of men is to make men more trustworthy. Men telling women they have no right to be afraid of them because it's sexist makes the problem worse because it reinforces the male-biased power balance.
There, Mansplained it for you. :D