Violence With A Point
When I was a kid, my Dad had very few reservations about me seeing rated R films. So long as it didn't contain any "satanic" elements, it was okay. I think he drew the line at taking me to see Pulp Fiction, but that's understandable since I was ten at the time.
The funny thing is that what I remember most about watching those films isn't necessarily the visceral violence, sometimes gratuitous nudity, and plot lines that were just understandable enough for a preteen. What I remember most were the discussions regarding the context of what we were watching.
Take Braveheart for example; Mel Gibson's sweeping historical epic about Sir William Wallace and the bloody path he carved in the name of Scottish freedom. The film is awash in slit throats, severed limbs, institutionalized rape, and that's just in the first act.
But my Dad made sure that wasn't all I saw. Beneath the viscera and brief nudity, there was a story about passionate and flawed people doing the best they could where history had dropped them. The protagonist wasn't successful just because of his brutality or moral righteousness. He won because he was smart. He consistently out-thought and out-planned a vastly superior foe because of this and the constant underestimations of his enemies. I was always given some sort of takeaway like this that made me think critically rather than take in all the mature content at face value.
Another example is Ellen Ripley in Alien. The audience is never under the illusion that she isn't scared. She knows just as well as us that she's in way over her head. It's her ability to control herself and do what's needed in the face of that fear. She never surrendered to the impulse to just give up and hide or act in a rash and poorly thought out way. This is the primary trait that carries her through her adventures and my Dad made sure I knew it.
A contrast point would be what's happened to the Die Hard series. For the first two, arguably three films, John McClane is meant to be all but a satire of the uber-macho supernaturally adept muscle bound no-nonsense action hero. He cracked wise, got his ass kicked plenty, and managed to scrape buy on unpredictability and cleverness. He was like a cross between Dirty Harry and Spider-Man. By the fourth film though, he has become that which he used to mock. He's involved in so many ridiculously improbable close calls, he's basically walking plot armor.
These takeaways apply to a slew of other such films we watched and discussed together. Action films aren't typically where one looks for life lessons, but if you look hard enough, you'd be surprised what you'll see with some reflection. This was my Dad's way of teaching me that self-control, mindfulness, and diligence could overcome other more superficial advantages. Kyle Reese vs. The Terminator, the Wolverines against the Soviet occupation (or North Korean; whatever), and even more dated stories of this nature such as David & Goliath all share this theme, and it's an important one now more than ever.