I have a few IBM ThinkPads from the 1990s, and they had a rubberized sort of finish to them that feels sticky to the touch now. How should I realistically go about cleaning them such that they won't be destroyed or look uneven in their finish?
Short version: use 70% IPA (isopropyl alcohol, A.K.A. rubbing alcohol) and cotton pads. Higher concentration IPA should be fine too, but isn't necessary. Gently rub the sticky mess with a cotton pad soaked in IPA solution, let the surface dry fully between passes, repeat until sufficiently clean.
TL;DR: The body of the ThinkPads produced in early to mid-90s is usually based on what appears to be ABS plastic, late 90s to early 2000s - a mix of ABS plastic and metal alloys, typically magnesium-aluminium (e.g., T20-T23 and A20-A22 series have magnesium-aluminium lid and plastic lower bodies, 770 series have metal lower bodies - not sure about their lid), later 2000s until around 2015 - again ABS plastic on the outside (often reinforced with carbon fiber or fiberglass in the lid) with magnesium-aluminium alloys used for internal frame. Up until recently ThinkPads had a separate coating made out of a polyurethane-based rubber-like polymer that aims to be self-healing - prior to late 90s it was used to cover the whole laptop, since late 90s (when IBM switched to using letters for designating families instead of numbers - e.g., A-series instead of 7XX, T-series instead of 600, etc.) they used that coating only on the lids, and AFAIK around 2015 Lenovo started phasing out the use of that coating altogether, though it's been a while since I pulled out my P50 and P51.
The problem with that polyurethane coating is that under certain conditions it degrades. I'm not sure what those conditions are exactly - some people suggest it may have to do with oils, high humidity and temperature, or exposure to sunlight. When it degrades it becomes more pliable and tacky than intended - those are the very same properties that allow the coating to be self-healing when they're present in moderation. Unfortunately, this degradation is a change in chemical structure of the material - AFAIK, it comes from polymer chains getting shorter. As far as I know there isn't anything that can be done in-situ to restore the material's original properties, so if the coating on your ThinkPad became tacky your only recourse, I'm afraid, is to clean it off.
I got a 701C with the original IBM bag made of bonded leather, and that bag just leaves black sticky residue on everything it touches, the fake bonded leather pretty much just falling apart into chunks of leather fibers soaked with polyurethane. The coating on that 701C was in the same condition - you take the laptop in your hands and you get black sticky mess all over your fingers. I'm afraid if your coating reached that point there isn't anything you can do about it except to strip the sticky layers. In case of my 701C I used isopropyl alcohol with cotton pads to clean it. I ended up eventually stripping it completely because after removing just the sticky layers it looked very patchy and ugly, but YMMV.
You shouldn't need to use anything more harsh than IPA, and 70% solution is good enough to get the job done. Please don't use anything containing acetone, MEK, or similar solvents, as those will outright dissolve the plastic underneath. Keep in mind that high concentration alcohols can cause some discoloration and minor damage to ABS plastic as well, especially at high temperatures and long exposure times, so don't soak the parts in alcohol and don't heat either the parts or the cleaning solution. But in my experience there were no major side effects of using 70% IPA to clean my 701C and let it fully dry between individual passes.
Your choice is one of sticky or ugly.
There is no nice solution. The only way to make it less sticky is to remove it, which will always also attack the body below. The body is (usually) based on the same type of plastics, thus solvable (aka attacked) by the very same solvent usable to remove the surface coat.
To do so various solution can be used. From ethanol to isopropyl alcohol all the way to paint thinner.
The core problem in doing so is that application must be as even as possible, and related to the amount of material to be taken off. This can be done in essentially two ways.
'Rubbing' with a Solution and Linen
Here the solution used is applied only in small amounts and rubbed off right away. It works a bit like sanding, like taking off skin with a sand-soap-mixture. The downside is that it will almost always result in an uneven surface, although this can be aesthetic as well :)) Resulting surface depends a lot on timing.
Pasteify the Solvent
Another way to apply it in a (more) even fashion is by turning it into a paste. This can be done by using a water-soluble solvent such as isopropyl alcohol and mix it with water and corn starch. This can be applied, dried and, depending on mixture, rubbed away or pulled off. The resulting surface depends much on prior condition (which usually is already uneven) and mixture. So not really something to be done without prior experiments to find the right one.
Bottom line: Keeping the original texture and operating it is next to impossible.
Bit of frame challenge here, but if your goal is just that they are 1) not sticky, 2) not damaged, 3) not uneven in finish...
Add a vinyl wrap over top of the sticky plastic. If you can't find a pre-cut one for your exact model, just get a sheet of adhesive-backed vinyl and a hobby knife and cut to size.
As a bonus, you also get a wide array of colors, prints, and finishes to choose from--either to recreate the look of the original or to go with something completely different.
I had that on a Logitech keyboard, at the wrist rest. I ended up just flinging the removed rest into the washing machine. Came up a treat! Perhaps I just got lucky since it had been sticky for 5 or so years (I used it little). I would not recommend stuffing the laptop in there and seeing what happens...
Lighter fluids like Zippo (basically naphtha) gets rid of sticky residue and grease much better than IPA 90% of the time, just dab a little on a rag and rub the goo off leaving a smooth plastic surface.
Depending on the type of coating though, sometimes even naphtha alone might not be able to do the job, might have to break out the scouring sponge for those cases