I'm not the most experienced player, but I figured I could take a crack at going down the viability rankings (at least the S and A tiers) and grouping the Pokemon into the three categories presented here.
9) Which Pokemon in the SS CAP Metagame have a natural advantage against Color Change due to the sets they are known to commonly run?
Doom Desire/Flash Cannon -> Earth Power
Aura Sphere/Focus Blast -> Stored Power/Fleur Cannon. Ignoring Steel here because I don't see Flash Cannon very often.
Sludge Bomb -> Future Sight. Alternatively, Flamethrower/Fire Blast -> Scald/Hydro Pump.
Aura Sphere -> Hurricane
Focus Blast -> Hurricane
Both of its STABs (Ghost and Dragon) are super effective against themselves. The caveat is that Color Change will likely gain an advantage from switching into a coverage move on choiced sets (Fire Blast/Thunderbolt).
Switching into Scale Shot lines you up for another super effective hit, as does Stone Edge/Fire coverage -> Earthquake.
Magma Storm -> Earth Power
Surf -> Volt Switch/Thunderbolt
Stone Edge -> Earthquake on SD (or even suicide lead) sets
Hurricane -> Thunderbolt
Often choiced, but Focus Blast -> Moonblast is a possibility on Boots sets.
I'm putting this here because sets locked into Draco Meteor are capable of claiming a kill, but this is iffy because Psychic/Mystical Fire are self-resisted and Aura Sphere is neutral.
Iron Head -> Earthquake
Not really an offensive mon, but Fire STAB -> Scorching Sands does sting.
Shadow Ball chains into itself
Bullet Punch -> Drain Punch. Alternatively, Drain Punch -> Acrobatics. This is kind of iffy because you're probably not hard switching into Cawmodore when it's boosted.
Close Combat -> Acrobatics
Spirit Shackle and Outrage chain into themselves.
Earthquake -> Flip Turn. Doesn't particularly care otherwise.
Similar to Swampert, Ground STAB -> Scald. Doesn't really care otherwise, though.
Meteor Beam/Paleo Wave -> Earth Power
Follow the circle of Weather Ball (in sun) -> Earth Power -> Giga Drain -> Weather Ball. Alternatively, Grass STAB -> Sludge Bomb.
10) Which Pokemon in the SS CAP Metagame are indifferent to Color Change due to the role they perform on a team?
Technically, High Jump Kick -> Zen Headbutt is an interaction, but the common Cinderace moves (Pyro Ball/High Jump Kick/U-turn/Gunk Shot) don't have super-effective interactions that can actually be capitalized. More likely, Cinderace will U-turn out or potentially outright KO with neutral hits, but this isn't particularly an advantage.
This is subject to change, given the nerf discussions, but based purely on its current role, the only thing it is discouraged from doing is Fire Lash spam. Its tools as an offensive utility Pokemon mean it isn't exactly impeded by Color Change.
Moonblast doesn't resist itself, and its other utility isn't blocked.
Scald spam can still burn, even if it resists itself. We can potentially resist a second Future Sight after taking the first one, but I doubt either mon is staying in long enough for this to be reliable. Otherwise unhindered.
Subject to change due to Spectrier voting. It can't spam Dark Pulse, but it does have another move in Earth Power to switch to, and it can generally Defog and Roost unimpeded. I've occasionally seen U-turn, which sets up Dark Pulse -> U-turn, but it doesn't seem to be common right now.
Double-Iron Bash -> Earthquake exists, but this is technically a win because a super-effective Earthquake does less than a neutral Double-Iron Bash. Band sets are disadvantaged enough (especially with Double-Iron Bash being self-resisted) to put it in neutral.
Potentially dislikes having Hydro Pump resisted, but is perfectly fine spamming its utility (including Scald) and Fairy coverage.
Taking Poison Jab is nice for the resistance and poison status immunity, but otherwise completely indifferent.
Crunch is self-resisted, Rock Blast means getting to ignore Sand damage for a turn, and Superpower doesn't combo into itself super well, but Superpower comboing into either STAB (i.e. Rock Blast -> Superpower) is not a good time.
May potentially regret using Seismic Toss, then getting hit by a Fighting move, and the fact that it usually runs many non-damaging moves means we can preserve our typing for longer, but is otherwise generally unhindered in its role.
Taking Power Whip means you can dodge Leech Seed, and taking Gyro Ball means resisting both a second Gyro Ball and Power Whip, but otherwise Ferrothorn can do its job.
Sheer Force ignores Color Change entirely, which means Nidoking is indifferent because it can't proc it.
Same as its Johtonian sibling.
I would argue that resisting Knock doesn't matter a whole lot when the first hit is what matters, and Earthquake exists anyways. There's the potential for Knock Off -> U-turn, but offensive sets are not very common right now. Doesn't care much otherwise.
It's capable of Defogging fine, and Dark move -> U-turn is feasible for a chunk, but if it lacks U-turn it's in a bad spot.
Straight up does not care, although getting to tank consecutive Hydro Pumps is nice.
I've never seen Body Press and Brave Bird on the same set, and Corviknight does not care otherwise (unless it's running Iron Head for some reason).
This is a weird setup against Scarf. Tanking Leaf Storm is very nice, but Focus Blast and Moonblast both don't care and Healing Wish is obviously a wash.
Draco Meteor chain is potentially dangerous, as well as Earth Power -> Freeze-Dry, but Ice self-resists otherwise on choice sets, so this is potentially a wash.
Giga Drain -> Sludge Bomb, though its role means it generally doesn't care, and not being able to Spore after a Giga Drain is annoying.
Knock Off -> Circle Throw potentially, although its role means it doesn't really care.
Here for the same reason Melmetal is here. Draco can chain into itself, and there's Bolt Beak -> Earthquake, but a super-effective Earthquake is outdamaged by a neutral Bolt Beak.
Doesn't care at all, both due to role and due to Earthquake's neutrality against itself.
Putting it here because the most common set will probably just U-turn out, but Choice sets are stuck being self-resisted on their Electric attacks.
Resisting repeated Lava Plumes and avoiding future burns is nice, but because of its role Torkoal generally doesn't care unless it's the last mon standing.
Similar to Cinderace. Close Combat -> Play Rough technically exists, but more than likely it will just Volt Switch out (and we do get a resist if it used Plasma Fists first).
11) Which Pokemon in the SS CAP Metagame have a natural disadvantage against Color Change due to the sets they are known to commonly run?
Best blocks Band sets, as Color Change allows it to resist Knock Off/Grass moves. The potential for Grass move -> U-turn/Acrobatics does exist, though it seems to be less common.
It's being put here because of Liquidation, and resisting Psychic Fangs is also nice, but Close Combat is a wash and Flip Turn means it gets out anyways.
Actually kind of funky. Draco Meteor being chained is potentially a problem, but both of its other moves (Thunderbolt and Fire coverage) self resist, and taking a Draco means that a second Draco is necessary (as both coverage moves are resisted now), and Cyclohm is probably not doing much otherwise.
Put here because self-resisting STABs on choice sets is good for us. However, Knock Off/Smart Strike -> Sacred Sword does exist on Life Orb.
I had trouble placing this mon, though I ultimately put it here because resisting multiple Scalds is really nice.
Technically Focus Blast -> STAB exists, but it's choiced most of the time, and resisting a second Psychic move is nice.
Electric is self-resisting.
Most sets are choiced, none of the attacks combo into each other super well, and Ice is self-resisting. The rare Boots set may be able to combo Ground coverage -> Ice STAB, though.
Coming in on Surging Strikes is really nice for blocking further damage, although the rare Protective Pads set could potentially get some damage in still. Neutral otherwise.
Choiced sets are stuck because all of their common moves are self-resisting, or U-turn. Boots sets get to strike neutrally, though.
This first look is not particularly inspiring, although these are also the best Pokemon in the metagame. I also didn't do much to distinguish Choiced sets from other, more flexible sets, which is where Color Change can potentially gain a big advantage. To be fair, some of these choiced Pokemon are usually spamming non-self-resisting moves (Specs Kerfluffle and Scarf Landorus-T, and to a lesser extent Specs Dragapult and Specs Magearna), but I may have missed some details, and hopefully this is a decent starting point. I may come back to do the B tiers in a separate post.
Changelog:
Edit 1:
Moved Tyranitar from natural disadvantage to neutral. Tyranitar actually runs Superpower way more commonly than I thought in order to not lose to Equilibra, which is a problem when comboed into any combination of STABs.
Moved Melmetal from natural advantage to neutral. It was pointed out that forcing Melmetal to EQ is still a win, since a super-effective EQ does less than a neutral Double-Iron Bash. Band sets are disadvantaged enough (especially with Double-Iron Bash being self-resisted) to put it in neutral.
Moved Nidoking to neutral. As
Marty pointed out, Sheer Force ignores Color Change entirely.
Edit 2:
Added B tiers. More of these mons use choice items frequently, often to their detriment. Tried to be as consistent as possible, although there may be some things that don't line up. Mostly agree with quziel's conclusion that we have a decent set of neutral matchups and deal well with the elementals.