I've only been going to Disney parks for a little less than 20 years, so I can't say much for sake of truly "classic" rides. I can, however, speak from the fact that's basically my entire life, so I have a lot of sentimentality toward some of these rides shutting down that have been around as long as I can remember.
I'll miss both GMR & EUOE dearly for sure. I remember I went on GMR for the first time when I was 6 and was absolutely scared to death from the Xenomorph, and never wanting to go on a dark ride again. It was always a great story to tell friends when visiting or just talking about the parks, though. For EUOE, I was completely enchanted the first time I went on and would give a play-by-play of the entire ride to anyone that would listen.
That being said, I understand why they're leaving. Both are clearly outdated. Hollywood Studios doesn't feel like Hollywood Studios anymore, so I'm guessing they're trying to re-brand and get things more cohesive before the name's officially changed. No truly classic rides should be in trouble, especially for Magic Kingdom. I feel like most other parks are up for debate as far as rides though with the surge in popularity at Universal Studios. Their 'no sacred cows' mindset has been working pretty well, so I'm sure Disney's weighing their options outside of MK (except for hopefully Stitch).
Oddly enough when I went to the doctor (and take this with an absolute grain of salt, I have no confirmation on this past her own word), I had a conversation with one of the nurses about how one of her friends worked on Journey Into Imagination and how she got to be one of the 'test riders'. In hindsight I should've asked more, I'm not even sure if she meant the 2002 or 1983 iteration. Regardless, she offhandedly mentioned that her friend said that it's slated for closing. It's pretty much on the same level as GMR & EUOE in terms of being outdated really, it just needs a complete overhaul at this point in my opinion. Not to mention it scared me just as much as GMR when I was a kid!
Basically I think the classic-classic rides are in no trouble at all. But with this current trend, we should definitely appreciate the less-popular rides before they're inevitably closed for bigger and (hopefully) better things.