It doesn't bother me in the least. I'm not saying that there's something wrong if it bothers you, but I tend to see people who can deal with things in the context of the time they were made and those who can't. The people who can't handle watching black and white movies, or who can't read a book that wasn't "changed for a modern audience". Or, I guess, more recently, people who can't handle watching movies that aren't in 4k because they're "not good enough". I don't care. Scratchy old VHS quality is fine for me if that's what it is. Old black-and-white movies from the 30s with mono sound, it's fine. Heck, silent movies are good. It's about the quality of the product, not the flash that matters. If I can see it and enjoy it, it's good.
It depends a ton on the core game for me. It also depends on whether I played it back when it came out and still hold fondness for it, or if I'm brand new to it.
Examples of older games I tried and could not get into:
- Sniper Elite 1.
- Deus Ex 1.
- Psychonauts (might give that one another shot)
- Escape from Monkey Island
- F.E.A.R. 1
- Blood 2
I bounced off of each of those partially because of the look of the games, but also because of other aspects. Sniper Elite 1 I hated the controls and general mission design. Deus Ex 1 had GODAWFUL voice acting. I mean, really painfully bad stuff. Psychonauts was too low-res on my modern rig. Escape from Monkey Island had horrible animation and worse controls, mandating using a gamepad on a series of games that were historically mouse+keyboard based. F.E.A.R. 1 just felt kinda blah. Blood 2 was similar.
But each of these games also had graphics that were incredibly off-putting.
Mind you, a lot of other older games I have zero problems with. I'll happily fire up the old SSI Gold Box games. My kid and I just played through Loom, Day of the Tentacle, and Monkey Island 2. I still love the old X-Wing and TIE Fighter games, as I do the old Wing Commander games.
But (1) I have history with those games, and (2) their art styles seem (to me) to be less prone to "uncanny valley" issues. The X-Wing games are a little like that, but the pixel art of the old LucasArts adventure games is perfectly fine. I mean, yes, it looks old, but it doesn't bother me. Likewise, I have no issues with black-and-white films. What I think can be harder to take, though, are older design conventions beyond just the surface-level looks. Control schemes, inventory mechanisms, "No, wrong, do it again" style difficult where a game's length is mostly down to you repeatedly failing at playing it, etc. For films, it's things like the soundtrack completely dropping out, static head-on framing like you're watching a stage play, slow pacing, etc. In some cases, I don't care because the core of what's there is still worth it, but there's plenty of instances where what may have been great at the time just...hasn't aged and it isn't "timeless."