Fair enough. I suppose the bottom line is that we don't know, on the available evidence, why they cause crime to go down (I personally didn't even know that they did, and remain not entirely convinced. I rather suspect any effect either way is negligible). One very simple thought that occurs to me is that if they open in areas where there is not a lot of other nightlife, and stay open late, they increase the number of night hours when there are lights on and people around. But I admit that is just conjecture.
If they cause crime to go down because they are diverting the kind of behaviour that leads to sexual crime into a sanctioned environment then that is also bad because, obviously, that proves that the clubs are all about the kind of attitudes to women that are sexist, mysogynistic and dangerous.
I'm not sure what you mean by "the kind of behaviour that leads to sexual crime". Sexual crime itself is, by definition, a behaviour. Touching someone intimately without their permission is a crime; doing so with their permission isn't. I'm not sure if anyone has successfully defined what behaviour "leads to" the behaviour of the crime, as prior to committing it the criminal could have been doing just about anything.
If it's true, as has been claimed earlier, that most clubs do enforce the no-touching rule for fear of legal consequences if they don't, then the only kinds of behaviour or attitude being exercised in the clubs are looking, conversing and thinking. Now let's suppose for the sake of argument that those things are happening in the "worst" possible way according to feminist principles - that the men are completely "objectifying" the women and living out their most lurid misogynistic fantasies through them.
If we then find that actual sexual crime (eg assault, flashing etc) in the area has gone down, wouldn't that disprove the very idea that "objectifying" via looking, thinking and fantasizing automatically leads to such crime?