Just to be absolutely clear about what we are discussing here:
What counts as evidence (anything that is known using our senses, repeatedly and in different times/locations) - repeated observations of things
What does not count as evidence - what somebody may have thought, seen or heard... once... and they may not even be sure (Father Ted and BIshop Brennan's image on the skirting board comes to mind)
For example, take English law on rape. It used to be the case, not so long ago, that in a rape trial, judges had to warn juries about the possibility that the female victim may be lying (sound familiar?). However, repeated observations (in the form of statistical generalisations) have shown that women do not lie about having been raped any more frequently than anyone lies about a crime when they are reporting it (that is, about 2-4% of all reported crimes are false allegations). The old warning is a hangover from pre-Enlightenment, pre-scientific, pre-evidence-based religious dictacts (women are less intelligent than men, more emotional, flighty, likely to change their mind, unreliable), which governed law making at that time. However, we have now got rid of this 'warning'. Something didn't make sense, we gathered evidence and on the basis of that evidence, we changed it. You can see why this is a reasonable way to proceed, and how scientific thought has rescued us. Indeed, it would be pretty silly to base a whole legal system on, for example, an old granny's thoughts about black men and crime or an old man's thoughts about women's slutty and slatternly ways... wouldn't it?
Another example. Take 'breast ironing', putting sand in your vagina during sex in NA cultures to 'dry' them, or, closer to home, smoking when pregnant. Statistical evidence (that is, evidence based on repeated observations) shows that the outcomes are measurable and negative. Not just hearsay or what a single (weird) individual thinks may be the case, but observable and measurable. And they are harmful.
The point is that it doesn't really matter that some people still think that women lie about rape, or still think that it's a good thing to 'dry' your vagina or 'iron' young girls' breasts. Who gives a crap as long as these thoughts go no further than what you think about these issues (Sport's example above). The key factor is that our official agencies do not think this, so that if someone turns up at a hospital wanting their daughter's breasts 'ironed' they'll be told 'No', or if a jury member thinks that the woman lied about being raped, it doesn't matter, because their thinking will not play any role in the official process and outcome (please don't tell me that this does not really happen. We are making these changes and that is all that matters; not how perfect the system is in actuality). .
I am utterly baffled (as somebody upthread has said) as to why we are affording equal credibility to non-evidence based outcomes as evidence-based ones in our legal, health, financial and political systems. I am also baffled at the growing influence of fundamentalist Islam despite ever increasing, sound sources of knowledge being more widely available than ever before. It doesn't take much to note that the striking similarity of ways in which women and their sexuality are and have been viewed in very different cultures, with their different gods, infrastructure and cultural conditions, is more suggestive of the hand of patriarchy, rather than the hand of god - all of which leads to my main point; who or what is allowing this to happen?