The objective evidence is rather clear that the Right has the greatest appeal to White Nationalists, Neo-nazis, and those with extreme reactionary views. No real shock there. Xenophobia, nationalism, paranoia and anger management all characterize many in the pro-gun advocacy so it does not take much to connect the dots.
I would actually take that a step further. I would want the company/software performing the background check to automatically generate am email to ICE when an illegal is flagged in the system. I don't believe that it is a good idea to let them buy guns in the first place. It creates an officer safety issue, should they be picked up.