Multiple Card Challenge

{Spoiler}{miku}Keyword: Cooperate is a fun and nice mechanic for team formats. I really like the idea of casting an expensive spell ahead of curve for the cost of your teammate's mana.

Enter the Service: While in monoplayer worse than Raise the Alarm, it's a slightly better one in THG. I guess it really shines in Archenemy.

Grouping Slimes: Blessings of Nature on legs. Looks balanced and fun.

Erin: Yes, the mandatory "Your cards have <new keyword>." I like this one very much. It has reasonable cost and still a good body, since granting cooperate can hardly get out of hand.
I think it could say "Spells you cast have cooperate."

{Spoiler}{kinotherapy}Keyword: Very simple and straightforward ability that rewards aggression.

Reckless Insurgent, United We Rise & Torch the Square: Very basic designs that look balanced. I like that Torch the Square is an instant so you have to choose between cheap or reactive.

Inspiring Vagabond: Ties nicely together with Instigate. I like how he costs two to ensure you pay at least two mana for it. I think he'd still be good at five mana.

Angel of the Masses: It's kind of fun that it gets cheaper the better it gets. Pretty awesome for a 10 mana 4/4 flyer. I like that it grants the pump when entering and attacking without attacking the turn it enters.

Nice rebellion you got going on there.

{Not Safe for Anywhere}

Blue Lives Matter

Enchantment

Blue creatures you control have first strike when blocked by black creatures.

*****

Black Lives Matter

Enchantment

Black creatures you control have first strike when blocked by blue creatures.

{Spoiler}There's a lot that I could say here, but ultimately this is a poor, low effort execution of a tasteless joke so I don't really see the point in judging it. I think you knew when you posted it but still, please try a little harder next time.

{Spoiler}Simple, but likely overpowered: a haste enchantment is already worth 3 mana, so adding a stream of tokens is extremely powerful. Vigilance isn't usually as good as haste but just consider that Bitterblossom was once banned in modern, so like, higher cost maybe.

{Spoiler}Not sure if this was intentional, but these would make a lot more sense in the opposite colours. The black one is fine, and could probably be pushed further since colour hate is generally rather weak, but the white one is a complete color pie break, even though it's only 1 damage. If they're going to have different effects anyway, you could, say, make their black spells cost more cast. (Or "counter it unless its controller pays if you want to keep up the symmetry)

{Spoiler}Cool!! Green vs blue is I'd argue the enemy colour pair least explored as actually being "enemies", and when they are it's usually nature vs technology, so I really like this take. The flavour fits the cards and their mechanics cleanly, and I love how the second abilities are both solidly in colour despite being so similar. Having said all that, I reckon they're pretty overpowered, in particular Mindstrength (compare
Jace's Sanctum) so they would need to go up in mana cost or have some kind of limiter on the card draw. Also, I enjoy the difference of opinion on the flavortext.

{Spoiler}Having a white 1/3 against a red 3/1 is a nice idea. The Captain is, I think, much weaker in the general case than the Berserker, with a weaker body and less permanent removal, so in the case where they're good the Captain is likely better (and the higher toughness is nice to have on a banisher priest). Berserker should have a "you may" so that he doesn't berserk himself. I'm finding these hard to judge because they have a lot of little bits going on - ultimately I think I would like them more if one part were trimmed for simplicity's sake.

{Spoiler}Enchantments and planeswalkers shouldn't really be getting tapped which just leaves artifacts and creatures, so you can just spell that out. You could also cut the "if you do" by wording it as "tap up to one target ____". A flash 2/3 for 3 is already a great common, and adding the deeptap pushes it over the edge, so I think these could go up to uncommon. Green tapping things is a much harder to solve problem though since that's just not a thing green does

{Spoiler}The idea behind this contest is two cards opposing each other, but these seem to be both caring about colorless? Kind of strange, but let's see. Extraneous Invasion's first ability is costed about right, but the second one has a lot of issues: it goes infinite with itself (Clues are colorless permanents you know), so unless you want to write "colorless nonland, nontoken permanent" (or perhaps "colorless nonland, nonartifact permanent"? Might make more sense with your theme) it should probably just be "colorless creature". It's hard to judge how strong that would actually be without knowing what kinds of colorless creatures we're talking about, but it's probably too strong.

Native Defense is way out of color, I can see what the ability is trying to do but if you stop reading at ": Untap target creature" you might see the problem. You could limit it to creatures you don't control, but ultimate this is a mainly green ability and I'm not sure how this ties into defense (you could mirror Invasion with like " Target creature can't block colorless creatures this turn" but you'd have to change the flavour) Finally, red is the color that does the least investigating, so its second ability ought to be something different, though I don't know what. It's also missing "nonland" but I assume that's an oversight.

{Spoiler}Nice and straightforward. Distract the Darkness is either completely unplayable or excellent depending on whether it's hitting a black creature or not, whereas Impale the Believers is passable, though weak, in general and pretty good against white. I would like these more if they were more in line with each other, perhaps with the white card preventing untap on the next untap step, but hitting black creatures with less than a hard exile. If it were an instant, you could consider punishing attacking/blocking creatures, though making Impale the Believers an instant might push it over the edge.

{winner}Daij_Djan — Bodystrength / Mindstrength win my vote, which is the only vote that matters. Thanks for your pairs everyone xox

{Yoshi} Interesting mana rock cycle with hilarious flavor.

{notfoxwolf} Simple cycle, perfectly fitting for blue. The uncommon really shouldn't bounce two creatures, though.

{oddnanref} I'm happy you solved the +1/+1 & -1/-1 counter issue – except on the mythic. That aisde, I like the idea behind the cycle but have some issues with the individual cards (memory issues with the uncommon, rare looks really weak.

{Akai Ryu} I like Scouters, even though your cards look a bit busy. And that common really doesn't work as a hybrid card.

{BurningCreator} Nice and flavorful cycle – your mythic should get a nontoken or non-Spirit clause to prevent infinite sac outlets, though.

{And the winner is..} This is quite tough, actually – you really created some pretty nice cycles After some pondering, I decided to give @miku the win with Fleur as runner-up!