But a negative correlation can DISprove cause-and-effect.
Unfortunately even that isn't true: see Simpson's Paradox. Not to pick on you, but it is really tough to make strong assertions one way or the other based on social science data. I think the best we can do is a Bayesian approach; start with some prior assumption based on ideology and personal experience, then adjust that prior based on the results of scientific studies. So in parent poster's case, his prior is that guns are pretty good in society, so the reinforcing data point that more guns = less crime makes his belief stronger. Someone whose prior is that guns are bad should probably not be as affected by that data (and if they are being intellectually honest, it would lessen their conviction that guns are bad), and someone who really had no opinion (if you could find such a person!) should be slightly more positively disposed to guns with that data. Of course, another study will typically come out shortly thereafter saying the opposite, so unless you get a series of studies all going in one direction, science will typically not change people's minds.