There are two ways people can learn and change their mind on issues they already have an opinion: personal first-hand experience and realizing how unfounded their opinion is through exaggerated, negative association of their beliefs. Both require a degree of willingness to rethink everything.
After expressing a personal view or - like in this case - taken action based on an existing belief system, there's absolutely, positively no way to influence it by rational and exceedingly polite behavior. It's a pipe dream. It just reinforces the pattern; a behavior that's out of line doesn't have any negative consequences. Providing, of course, that this isn't about store policy, which question remains unanswered; considering that the greeter never called security or a manager, it's presumable that that is not the case.
A response that subjects the person in question to public ridicule is equally ineffective in changing opinions, but it most certainly affects the likelihood of the person in question repeating similar behavior in pavlovian terms. People respond to pain and pleasure, physical and mental alike, and change their behavioral patterns accordingly.
An example of what MIGHT have made the greeter rethink his/her approach could have been a third party, a bystander, joining him/her, exclaiming equal nonsense but in much more exaggerated manner ("You can't have a gun!" "Nobody should own guns!" "Are you here looking for someone to shoot and murder?!" etc.), subjecting the whole expressed point of view to a much broader, self-evident ridicule. Just risking being associated with a person behaving similarly is a massive wake-up call. This is the same philosophy that's behind an incentive of trying to call even moderately right-wing groups nazis; as a subjective claim it's preposterous and has little if anything to do with facts or reality, but the plain projection reflects the wishful thinking of the effect if it had.
I have a habit of taking every anti-gun person I meet in a social environment as a challenge. Acting even more fiercely anti-gun than they are (providing that they have no idea about your background) and escalating the claims further and further - all the way to having all military forces dismantled, disarming the police, forcible house to house searches for hidden guns and life or even death sentences for just possessing a firearm of any kind - eventually reaches the point when THEY are in the position of defending civil rights. After that it's just a matter of reeling it all back conversationally, step by step.
Exposing these mind [honk]ing techniques may not be the most ethical thing for me to do, but it's always a good idea to arm fellow gun enthusiasts with some basics of how to actually influence people. Dale Carnegie had a lot going for him but just being polite, interested and civilized doesn't quite cut it in today's polarized and self-identification based opinion environment.
So, was the OP's incident caused by store policy or not?