I don't think showing any film or tv series would actually change any minds.
Show them one that depicts some sort of SHTF invasion like Red Dawn, and an anti is likely to say "This isn't realistic. Any military with decent hardware would role right over citizens with small arms. And any country that didn't have advanced military hardware wouldn't try it in the US." or some variant of that. And honestly, I think they'd be exactly right. Any notion that "an armed citizenry should be feared by it's government" is totally absurd to me in the current day and age. Any military action in this country against it's citizens would be sweeping and unstoppable as long as the soldiers enacting such atrocities were following their orders.
Historic films that depict the need for the citizenry to be armed are very much realistic, but an anti would say "This could never happen now." They forget that rights can be taken away by whomever has the guns. I believe the cushiness of American living has lulled them into a false sense of security.
What many antigun people don't think about is that sometimes a crime being committed against you isn't necessarily about stealing. Sometimes it's about victimizing someone. Anyone remember what happened to the Petit family in 2007? The family complied and even went to a bank to retrieve MORE money for the perpetrators. But it still ended with the rape of two family members along with the murder of three helpless victims. That's pure evil. If you go digging for stories, it becomes apparent that even though violent crime is down in the country, there are still a lot of psychos out there that are undetected. Horrible, and I mean ungodly horrible things happen.
Evil exists. It can't be reasoned with. It can't always be easily recognized. And if you wait to see if you are only going to be robbed rather than murdered, you have waited too long to defend yourself. If you want an antigunner to listen, make them watch those real police file shows, or read some stories. Make them understand some bizarre Hollywood scenario isn't why we own guns, it's to protect against the undetected evil that walks the street.
Just one guy's opinion. Any film, tv, or audio story that isn't a documentary, and doesn't illustrate the fact that evil people exist, and you don't know if one will knock on your door is going to be ineffective. I apologize for not being in the spirit of this thread, but I just don't think there is anything out there that would effectively change minds or sentiments on gun ownership other than documentaries of horrible stories. Even "historic" films depicting real events are dramatizations. Facts need to be our tool.