Simple speak to them. Explain to them that although this is a simulation of military conflict, at the heart of it, its still just a game which has a great and friendly social circle.
Don't try to change their minds but try and get them to look at it in a different way, for instance its just a game and no one actually gets hurt, its not in anyway violent there are strict rules on any kind of physical or verbal confrontation. try to make clear to them that they are focusing on the negative connotations of what the hobby looks like and show them what it actually is.
Airsoft is much less violent than football, rugby, squash, or even hockey, All of which I've played and ended up with worse bruises & witnessed much more aggression in these sports, which is usually allowed to continue during play. We often act nervous about airsoft because of the gun thing but lets be honest at the end of the day, its basically a high end toy but this is not seen because people automatically think Airsoft is based on violence when it really isn't.
For instance my other half hates anything to do with the military and despises guns of any kind, but she see's that Airsoft is a fun pass time and totally gets the social aspect is great fun. She understands that the people involved are big kids who just want to have a day out having a laugh....nothing more. Because she understands the hobby as a silly day out playing army in the woods, she accepts it and has even fired my rifs. Just try to show your parents that its just a daft game where people get out, make new friends and get some exercise which is a lot more healthy than some of the stuff you could be getting up to sat in your room on the internet.
I for instance hate real guns, the idea of gun ownership freaks me out, but like I often say, "I'm an Airsoft nut, not a gun nut" and try to show them that although Airsoft looks violent, you cant judge anything by looks alone, that's a flawed way of looking at anything.
I hope this helps mate