I've never had a problem with watching movies from any year per se, but the film itself has to grab me. And that goes for genres too. I have favourites from all over the place, but I'd be lying if I said that I can sit through anything and everything. I can say that I like a certain aesthetic or theme, but not everything that falls under those banners will appeal to me. And I feel the same towards all "art", proper and just consumer-based, in general. It's why I never bothered to develop a music taste; if I like the way it sounds, I listen to it. If I like a movie, I watch it. I like movies set in the Antiquity. I enjoy the Old Hollywood Epics. But I can't sit through all the old flicks with that theme, like the countless Hercules and Goliath and so on movies. In a way, film is a medium that ages, especially compared to something like music and painting. The limitations of each age, the defining points and trends of the period, everything plays a part. In the old days you had practical effects, no CGI. Then they started using computers. Around the 2000s you had that turning point where the CG was good enough to do some wilder stuff, but still limited enough to warrant practical effects and setpieces. Now it's all done with CGI which makes movies feel extremelly artificial. Someone who got used to one style will find it hard to get into another. Movies being a mix of various things (sound, image, motion, etc), show their age, whereas a piece of music, a painting or a sculpture remain unchanged, and anyone can appreciate them.
Personally, I think, it's useless to make generlizations on periods over pieces of media. Nostalgia and the generational bracket play a hugely important role. You like things based on aesthetics and personal values that you might find in something from the 20s, the 60s and the 2010s. Or something might just "click". I've enjoyed Haxan, which is from 1922, but I'd be lying if I said that I can easily sit through all movies of that era. I like Drive, but that doesn't mean I love all of Refn's filmography. I've seen my fair share of Arthouse, and while I love some, I loathe others and hate the overindulgence in something that's quite useless as a genre. Some things just "click". The colour pallete, the actor(s), the themes, everything. Even directors aren't always consistent with their styles. I love the Coen Brothers, but NCFOM, A Serious Man, Intolerable Cruelty and Miller's Crossing are all wildly different. I watched The Man Who Wasn't There and enjoyed it, but moreso because of their style and the cast. If the same story wasn't told in that manner, I wouldn't have given it the time of the day. I like lots of Crime related movies, but I'm not a Gangster afficionado who gives every movie under that genre a chance. With art, highbrow and lowbrow, it's difficult to analse things properly and logically; some things appeal to you and some don't. Even in Capes, there are tons of variations of the same type, but it's only people who are hyperfocused on a particular one that like every such character; others pick and choose based on aesthetics. I like the Super Scientist type. I like Doom, Richards and Stark. But then you have Pym, Banner, Brashear and so on and so forth. They all have something I like, even on a basic level, but I can't just get invested in every single one of them. At some point I think it betrays a lack of genuine taste.
In the end, there are things that are timeless and things that are dated. Sometimes they're so dated they act as a time capsule and become sort of relics. Sometimes you can revolutionise something and still end up becoming outdated in the coming years. How that works on a macro-scale is different from how it works individually. For my money, the Indiana Jones movies are still enjoyable. I like Adventurers, things like Tomb Raider and Uncharted. That doesn't mean I care for those flicks where Michael Douglas hops around the jungle (green diamond or something). Indiana Jones just works. Maybe because I was introduced to it as a kid, maybe because of the craftsmanship of the effects, maybe Ford's charisma and so on. There were jungle movies before IJ, but that's the one that stuck. I can see someone finding them boring and outdated, the same way I really can't sit through hokey 50s Sci-Fi, even if Sci-Fi's generally my favourite genre; from Hard to Space Operas. Me, I'd want Hot Toys dollies of Drake, Indy and Lara to pose together. I'd play a new IJ game. At the grand scheme of things, it's a franchise I like, for this or that reason. But there are other "classic" franchises that I dont care for.
I think it'll be interesting to see how all these IPs fare in the next 50 years or so. Will Batman, Superman, Predator, Spider-Man, the X-Men, Halo and so on still exist? There was a time Halo was THE videogame, and now even CoD has been burried. "Classics" are left behind all the time, and there's very few pop culture media that I can see having the longevity of something like Frankenstein, let alone survive throughout the ages like the Iliad or Shakespeare.