It used to be that the only people with tattoos were old sailors who'd gotten drunk on shore leave, and prison gang members. It was the association of tattoos with criminal gangs that gave tattoos a bad rep in the first place. Of course today tattoos have become trendy and cool and just about everyone has them. But, it would be wise to remember how that came about. Popular culture has sunk to unprecedented low levels in art, music, clothing, and personal appearance. This has happened largely through the glorification of prison culture. It can be seen and heard in rap music, ill fitting clothing, and yes, tattoos. Prison issue pants don't fit, so they hang down low. Often belts and shoe laces are not issued. And prisoners cover themselves with tattoos for various crime related reasons.
So if you have tattoos you should expect law enforcement types to take a second look at you. Even though tattoos are common today, they still carry the traditional prison, gang, criminal association in the minds of conservative law and order types, especially the older ones. You might think that's unfair in your case. But you need to understand that by getting tattoos you bought into that whole pop culture originating from prisons and gangs. That is where it came from.
It is against the law for felons to possess guns. And, the police reasonably relate felons with those who have been in prison or in gangs. So, when they see guns and tattoos on the same person, it's understandable that their interest might be aroused.