A Crown of Stars: Avalon's army commanders Ching and Bir. Ching is the Red Oni -enthusiastic, mirthful and passionate- and he is the Blue Oni -calm, serious and somewhat staid-. They are also a Battle Couple.
Advice and Trust: Asuka and Rei. The differences between both become less extreme after Rei stops taking emotion-suppressor meds, but Asuka is still hot-blooded and impetuous and Rei is still quiet and calm. During the story their friendship develops and they become a very close-knit combat unit together with Shinji.
Blood and Honor: Vette - talkative, excitable, more at home in the underworld than anywhere else, wielding dual blasters and spending most of her free time in cantinas - versus Quinn - traditional, reserved, dedicated to the Empire and his duty, a consummate professional who looks down his nose at those he thinks are unprincipled or undisciplined.
The Child of Love: Asuka is the Red Oni and Rei the Blue one. Shinji compares them in the first chapter, saying Asuka is fierce and loud whereas Rei is calm and quiet.
Children of an Elder God: Asuka is the Red Oni -being fiery, high-spirited and loud- and Rei the Blue Oni -she is quieter, colder and usually emotionless-. As a bonus, Asuka has fire-related powers.
Doing It Right This Time: Asuka was the Red Oni -temperamental and impulsive- and Rei the Blue Oni -emotionless and quiet-. After returning to the past Asuka is calmer and Rei is learning to recognize and express her emotions, so differences between both are less extreme, but Asuka is still the passionate half of the duo and Rei the calm one.
Dungeon Keeper Ami features Jadite and Ami, occasionally. Jadeite also fills the same role to Cathy. On the other hand, Tiger is a red oni to everyone, even Jadeite.
Evangelion 303: Asuka is the Red Oni -she is hot-tempered, hot-headed, loud, boisterous, proud and impulsive-, and Shinji is the Blue Oni -calm, modest, quiet, patient, wary, understanding-. They are a Battle Couple.
In Ghosts of Evangelion Asuka is the Red to Shinji's Blue. She is hot-blooded, quick-tempered and impetuous, and Shinji is calm, rational and passive. She helps him be more assertive and he keeps her calm.
HERZ: Asuka is the red oni (she is temperamental, rash and hot-headed) and Rei the blue one (she is calm and soft-spoken). Due to their clashing personalities there was some hostility between them when they were young, but after twelve years it has mostly faded.
Higher Learning: Asuka and Shinji were this for a long time. They were always together, and Asuka was the hot-headed, enthusiastic Red Oni and Shinji the quiet, meek Blue Oni. This changed after Asuka's Mind Rape, and she became silent and gloomy.
Last Child of Krypton: Passionate and fiery Asuka is the Red Oni and collected and silent Rei is the Blue Oni. It was specially noticeable in scenes where Asuka reacted and acted while Rei prefered waiting and analyzing the situation.
Asuka and Shinji are like this. Asuka is the Red Oni -temperamental, bold and daring- is the Shinji is the Blue -tranquil and quiet even when he is angry-.
Rei -calm, soft-spoken- is also the Blue Oni to Asuka's Red one. Due to Shinji changing the timeline events they unexpectedly become friends, and better teammates (and Rei actually saves Asuka's from dying inside a volcano.
The One I Love Is: Asuka -Hot-Blooded, hot-headed, angry, loud- and Rei -emotionless, detached, calm, quiet-. Their relationship greatly evolves throughout the story. At the beginning Asuka detests Rei and Rei ignores Asuka. Later, when they start competing over Shinji, they can not stand each other. Finally, after a violent fight, they make up, call a truce, and they gradually become friends.
Adell can also, arguably, qualify as the red oni to Mao's blue oni.
What About Witch Queen? has two pairs like this on opposite sides of war. On Arendelle side, general Kristiani is impulsive, "let's crush them now" red to Olafsen's more careful blue. On Weselton side, general Potter is red with More Dakka approach, while general Windsor is blue and described as "cold-blooded, sneaky bastard" by one of the Arendellans.
The dynamic between Chaos and Takato in the Tamers Forever Series is an interesting inversion of this trope. ChaosGallantmon has blue highlights on his armour, while Gallantmon has red highlights, and Chaos is also much more ruthless than Takato, but surprisingly enough, Takato is actually the Blue Oni, being much more subtle and thoughtful than the impulsive Chaos.
Peace Forged in Fire plays this contrast between Rahaen'Enriov D'trel ir'Aehallhah t'Rihannsu and Khre'Riov Morgaiah "Morgan" ir'Sheratan t'Thavrau, the two lead members of the Romulan Republic diplomatic team. D'trel doesn't like Velal, the Praetor of the Romulan Star Empire, and has diametrically opposed political views, and runs on Unstoppable Rage in battle, while Morgan is a more traditionalist Romulan, shares a friendly drink with Velal to hold the negotiations together, and has a much calmer, more rational fighting style. Also visible in their ship choices: D'trel's Kholhr is a Glass Cannon/Fragile SpeedsterT'varo-class light warbird, while Morgan captains a Mighty GlacierD'deridex-class battlecruiser.
In contrast to the source material, in Traveler, Ash is blue to Gary's red. He serves a similar role to his early travelling companion Jonathan. Lance and Steven's relationship has tones of this, with Lance as red and Steven as blue.
Appropriately, among Ash's Pokemon, Infernus plays the red to Torrent's (post-evolution) blue.
The Snow Has Stopped The Rain has Zangetsu, who's crude, violent and hot-blooded (red) and Shirayuki who is (usually) calm, collected and proper (blue).
Wonderful has Taylor, who is the Red to Emma’s Blue. The former is bold and loud whereas the latter is calm and rational. Emma often helps to keep Taylor grounded.
Asuka is the red oni and Rei the blue one. Reinforced because Asuka's powers are fueled by fury and fierceness, and Rei's by joy and despair.
Shinji is also the blue to Asuka's red. She is a furious, passionate physical fighter. He is a calm, conniving schemer.
In The Second Try, Asuka is the Red Oni to Shinji's Blue. Although she's calmer and he's less timid due to their increased maturity, she's still daring, bold and passionate whereas he tries to be a calming, pacifying influence.
The crossover Crossfire has Vash and Brandon as the Red and the Blue respectively. Vash is a loud, cheerful donut-loving goofball who always tries to resolve every conflict peacefully. His favorite flower is red geranium, and when he somehow gets in a fight, he will always find a way out with various tricks. On the other hand, Brandon is a cool and quiet undead mobster who won't hesitate to injure or even kill people when it's necessary to resolve a conflict. His favorite flower is forget-me-not, and whenever he gets in a fight, he tends to bulldoze everything in his path with brute strength.
In Cardcaptor Rad, there's eager and passionate Hot Shot whose something od a Blood Knight, and calm, meticulous Red Alert, who'd rather wait and plan things out. Unsurprisingly they clash a lot.