Twin sisters of the Nasu Verse, Aoko and Touko, are this. One is chaotic, the other lawful. Touko was originally depicted as having blue hair until the Kara no KyoukaiOAV gave her an Adaptation Dye-Job to resemble her twin sister more. Genetics beats out symbolism these days. Nevertheless, their Mage Titles are "Red" and "Blue". (Don't bring it up, it's a sore subject.)
Inverted in terms of their titles. Aoko exhibit the traits of red but her title is "Blue" (since the color blue is associated with her magic) and visa versa for Touko. Aoko's name also comes from the Japanese word for blue, "Aoi."
Slightly played also with Archer and Lancer by their color scheme, but their personalities are exactly the opposite.
Shirou and Archer are practically a textbook example. Shirou is emotive and driven entirely by his desire to save everyone and ensure that no one is hurt that he is there to save, which makes him easy to manipulate in some cases. Archer is utterly goal-oriented and makes cold, rational decisions based on what has the highest chance of success - this is even reflected in his ability Eye of the Mind (True), which enables him to analyze a situation and plan tactics even in the heat of battle. Shirou is extremely protective of his friends and will prioritize their safety and the safety of civilians, including being willing to fight Caster on his own in Unlimited Blade Works to stop her from draining energy from the town even though he didn't stand a chance. Archer is practically For The Greater Good incarnate and will make sacrifices to achieve his ends, including letting Caster go even though he could have killed her because she was suited to take out Berserker and he could easily kill her after that. The critical moment where this really comes to a head is when Archer betrays Rin by offering to join Caster's side. Shirou recognizes that it was likely they only way they were leaving that situation alive but says he can never forgive Archer for betraying Rin's trust and loyalty like that. Archer saw it only as the best means for victory and did it with little, if any, remorse as he had already been playing (and winning) a round of Xanatos Speed Chess against pretty much everyone. Their friction in this regard is the main reason for their complete inability to get along on any route, which is sort of funny as they are actually the same person.
In Tsukihime, this seems to be the situation with twin maids Hisui and Kohaku, who are Polar Opposite Twins, with Hisui being the cold one, and Kohaku being the passionate one. But this is actually a subversion, with Hisui and Kohaku having switched personalities when they were younger.
Mion of Higurashi: When They Cry has a tattoo of a blue oni, prominently featured in the opening. However, she's far more like the red oni in terms of personality. Then again, the tattoo isn't "hers" to begin with, thanks to an unfortunate Twin Switch in which Shion was supposed to get it. As a result, Mion is supposed to act Red as part of the older sibling role she's forced to play, while her sister Shion acts Blue as part of the younger sibling's role. In truth, Mion's true self is blue while Shion's is red
Also, in episode 20 of Higurashi, Hanyuu says "If Keiichi is a flame that burns red, then Rena is a quiet, blue flame!"
Keiichi (red) also has this relationship with Mion (blue) to a lesser degree.
In Umineko: When They Cry, Lambdadelta is the red to Bernkastel's blue. In the first half of the series, anyway. In the second half, as their true motivations are revealed, their roles are switched around.
Shannon can be seen as the red to Kanon's blue most of the time, but when it comes to matters of love Shannon is more calm and collected while Kanon is more hot blooded and irritable. It is also heavily implied that they are in fact the same person, and their red and blue dynamic shows Yasu's conflicting views about love.
In Summer/Shiny Days, Kotonoha and Setsuna are literal "girl in red" and "girl in blue" respectively.
The Ace Attorney series has some Red and Blue Onis. An inverted example is Phoenix, the blue-clad defense attorney (who isn't as hot-headed as a typical Red Oni, but he doesn't tend to think things through) and his red-wearing frenemy Miles Edgeworth, who is calm, cool, and calculating most of the time. In fact, the lawyers with the more fiery reddish qualities (Phoenix, Franziska, etc.) have a blue motif in their dress, while the more aloof ones (Edgeworth, Godot's visor and clothing as Diego Armando) have a red motif.
Another example from the later game, Apollo Justice, has the title character wearing a red vest - his preference for the color red is even mentioned a couple times in-game - and being rather impulsive (also, his hair is horns!). There are a couple of blue onis in the game. Kristoph Gavin, for one, is, though friendly, very serious and icy as well and wears a blue suit. However, in the end, Kristoph pretty much out-hams every murderer in the series. Klavier Gavin is the epitome of "cool collectedness" and wears a purplish maroon getup.
Also from Apollo Justice, to a lesser degree, we have another inverted version with Klavier in his pinkish/reddish/purplish outfit as a cool straight-man, and his band-mate Daryan Crescend in a blue, shark-like outfit being quite temperamental.
Also played with in Justice For All: Matt Engarde, a popular - if somewhat dim - celebrity wears a scarlet jacket, whereas his manager, Adrian Andrews, is calm and collected and wears blue. In reality, Engarde is a vicious, self-obsessed manipulator and Adrian is a co-dependent, frail woman who's deathly afraid of Engarde.
Also, Hot-BloodedDumb Muscle Masato and his friend/rival, the Stoic, Kendo-playing Kengo. Fittingly, Masato wears a red shirt, while Kengo is almost always wearing his navy blue Kendo outfit.
Hatoful Boyfriend: the human girl is generally red to everyone else, with the exception of Oko San who matches her for hot blood. As brothers, Yuuya and Sakuya are red and blue respectively.
Remember11 has two protagonists: Kokoro, a girl who is reasonably smart and well-educated but also friendly, passionate when arguing, and has a tendency to jump to (often wrong) conclusions about things; and Satoru, a student of the natural sciences who tends to analyze everything with scientific methodology (but not cold—he can also be quite passionate when the situation calls for it). The colors are also made explicit in the Title Sequence: The two are seen passing by each other, where their whole bodies are tinted their respective colors. In another instance Kokoro is seen turning into Satoru; their eyes flash first red then blue.