ranging from gun nuts, to global warming deniers, creationists, etc.
Invariably, the person attempting to deny science has not a clue about the various ways that statisticians and social scientists have devised in order to distinguish non-causal or confounded correlations with causal links.
Yes, it is true that, as a matter of theory, it is impossible to draw causal conclusions by simply observing a system. But if we were to stop right there, that would mean that we could never draw any causal conclusions in any social sciences -- since you can't do clinical trials or perform controlled experiments -- and so we should just abandon the who enterprise of trying to reason empirically about large observable systems. This whole notion is very appealing to people who (a) are consistently on the wrong side of empirical evidence and (b) tend to trust their "gut" rather than data to begin with. In other words, people like right-wingers and gun nuts.
When it comes to gun violence, there is plenty of evidence beyond just raw correlations. For example, higher rates of gun ownership correlate with higher murder rates, this is well established. Of course, one can argue plausibly that there are non-causal explanations -- maybe people buy more guns when crime rates are higher, to protect themselves. Or maybe the rural lifestyle results in more violence for some non-gun related reason. However, on closer inspection, these other hypotheses fail. First, gun ownership does not correlate to other kinds of violent crime besides murder, something that pokes a hole virtually all of the alternate explanations (e.g. if the high homicide rate in the US were due to Americans being inherently violent, then we would also have high rates of robbery, rape, etc., but we don't). Also, the increase in murder rates associated with increased gun ownership is due to higher gun homicides -- rates of non-gun homicide are not affected.
And so on.
As a rule, with no exceptions I can think of, the gun nuts who throw out the "causation/correlation" line never have an intelligent alternate hypothesis for the empirical evidence. It's just an attempt to deny the obvious with a catchphrase they learned in junior high.