I remember not being allowed to watch R rated films when I was really young, like below 10? But I got a TV in my room pretty early so I snuck-watched whatever I wanted lol. During my early teens/tweens I recall things getting much more lax, although still a little controlled. Once I fully moved in with my mom around 7th grade I was basically given full reign to do whatever I wanted, though. Plus side of being a chill, behaved child with an easy going single parent. :^))
I don't plan to have kids, but if by some weird stroke of life I did, I'd probably follow a similar path -- although it'd highly depend on the kid's temperament and the movies in question of course. Like for myself, once I hit around 7/8 I never recall having any issues with media scaring or upsetting me -- I knew what was real and what wasn't so I never had any problems. But I def recall kids growing up that absolutely could not handle any kind of scary media (heck, I have a friend now like this). It'd really just all depend.