And yet it is also bigotry towards the innocent.

It is always interesting to see which prior probabilities are seen as acceptable for use and which are not. Humans have a very limited amount of time, and coupled with risk of physical danger, it should be expected for prior probabilities to be used. I would even go so far as to say necessary for long term survival.

In this case, given the long, well established history of the subjugation of women by men, I would say they are well within their rights to be "careful".