...and you haven't explained why there are any non-racist paranoids, particularly those who own guns more than average.
Paranoia comes in different situations. One can be paranoid about choking while eating a meal, so one counts the number of times one chews a mouthful of food.. Or, one can be paranoid about the day turning rainy, so one always carries an umbrella. One can be paranoid about people that one has heard might be less oriented towards civil behavior, so one wants to have a weapon in one's home. And, those less civil folks can correlate with tatoos, being loners, drifters, or even other races. In my opinion, gun owners might not want a gun, due to feelings of racism, but perhaps feelings of paranoia about Martians landing. The fact that a study correlated racism and gun ownership might not have focussed on a correlation between fear (aka, paranoia) of Martians invading, or of drifters, or of societal collapse, or of packs of feral dogs. So many things for a study to discern as the reason some people want a firearm. Racism might be a co-factor to many others fears, so isolating racism as the "link" might be just a false conclusion.