In Pocahontas The British Settlers and The American Indians this was cemented during the song "Savages."
In The Prince of Egypt, the Distant Duet "The Plagues" has Moses in orange light and Ramses in blue shadows at the end of the song. Their clothing choices throughout the film follow the same color scheme. It fits their overall personalities as well, with Moses being the impulsive and exuberant one that gets them both into trouble, and Rameses being the overly thoughtful, in-control type hailed as a great leader. (Though ultimately, Moses’s passionate nature results in empathy and compassion and enables him to save his people; whereas Rameses’s analytical, rule-following stoicism makes him cold and ruthless and causes his greatest fear—ruining his father’s legacy—to come to pass.)
There's also Tauriel and Legolas in the last two films. Tauriel can also be paired with Thranduil, who is also blue.
RedTails: The primary character conflict is between Hero/Lancer duo Easy and Lightning. Blue and Red respectively.
In the Hellboy series, the title character (sloppy, hot-tempered demon dating a human flamethrower) and Abe Sapien (studious, slightly prissy gillman) are actually addressed as "Red" and "Blue" respectively; although this is due to, y'know, their actual skin color, the association still fits. Hellboy and Krauss, too, particularly when Krauss is possessing that Golden Army trooper in the final scene - all his glowy bits go blue. They fit the personality portions of this trope to a T.
The Sith and the Jedi fits this trope to a T. The Sith wield red lightsabers and are defined by their passions and their ambitions. While the Jedi typically wield blue or green lightsabers and are presented as more intellectual and steeped in tradition.
On a more individual level, the master/apprentice relationship between Obi-Wan Kenobi and Anakin Skywalker during the prequel trilogy. Obi-Wan is the more cautious and thoughtful blue Jedi and Anakin, being younger and more ambitious, represents the passionate red. Of course, this speaks volumes about the paths the men choose by the end of the end of said trilogy.
Later (or earlier, depending on how you look at it), the trope is played with by Han and Luke. They switch roles as Character Development ensues: Luke starts out as the impulsive idealist to Han's world-weary cynic, while by the third film Luke is the disciplined and determined warrior and Han is the emotionally driven one.
In the movie version of L.A. Confidential, Edmund Exley is a near-perfect example of a blue oni (and nearly always dresses in a blue suit to boot), while Bud White is very much a red oni (complete with brown/maroon suit).
In Men In Black, Agent K is the serious, deadpan blue oni mentor while Agent J is the wisecracking, impulsive red oni rookie.
James Ellroy seems to love this trope; the two detectives at the center of his The Black Dahlia are even referred to explicitly as Mr Fire (red) and Mr Ice (Blue).
The Will Ferrell movie Blades of Glory has Chazz Michael Michaels, the improvisational, womanizing idiot Red Oni, and Jimmy Macelroy, the technical, thoughtful man-child Blue Oni. This is even reflected in their "Fire and Ice" costume.
From Watchmen, Rorschach/The Comedian/Ozymandias to Dr. Manhattan. Actually, everybody is a Red Oni compared to Dr. Manhattan.
A better example might be that Rorschach is Red Oni and Nite Owl II is Blue Oni.
Every Die Hard movie has one or more elements of this. John McClane, the hot headed runner and gunner always goes up against a calculating intellectual Big Bad. The first two movies also have a subplot involving McClane's "Red Oni" tactics budging up against the "Blue Oni" by-the-book style of the authority.
In Raiders of the Lost Ark, Belloq is the blue oni to Indy's red oni. This ties into their preferred methods for acquiring artifacts. Indy is hands-on and collects them personally. Belloq hires other people to do the dirty work while he stands off to the side acting sophisticated.
Osmosis Jones has this with a color inversion. Ozzy is the Red Oni and Drix is the Blue Oni. This is despite Ozzy being blue and Drix being red.
Straight-laced and collected Elinor is blue, while the flighty and passionate Marianne is red.
The men who court Marianne: Willoughby is fun and dashing, but false. Colonel Brandon is reserved but true.
Charlotte Palmer is bubbly and easily excitable, while her husband Mr. Palmer is quiet and sour.
Thor and Loki from Thor and The Avengers are the epitome of this trope. Although, given their colour schemes, it's more like Red Oni, Green Oni.
Another Avengers example would be Iron Man & Captain America. The brash and arrogant antics of the red-clad Iron Man really don't sit too well with the humble-natured and calm Captain America, who wears blue.
In the regular Iron Man films, James Rhodes is the blue Oni to Tony's red. And, like Rogers, he is usually seen wearing blue.
Another member of the Avengers who embodies both Onis is mild-mannered scientist Bruce Banner and his alter-ego the Hulk, who is literally a raging id.
In William Shakespeare's Romeo + Juliet, the Montegue men are Anglo guys in Hawaiian shirts who seem to be a bit more loose and rough. The Capulets are angrier, sharply-dressed Latinos.
In the 2011 film Warrior: Tommy is red, Brendan is blue. Their gloves are color-coded for your convenience.
Pulp Fictionzig zags this trope with Jules and Vincent. On the surface, the former is hotheaded and the latter is calmer, if not outright aloof. As the film progresses, it's quite clear that Jules is the one with the more level head and that his "Bad Motherfucker" tendencies appear only when someone (usually Vincent) says or does something really stupid. Vincent, on the other hand, is a bumbler, needlessly starting a brief argument with the Wolf when presented with advice to solve a problem he started and leaving dangerous stuff around for people to find (Mia with the drugs, Butch with the sub-machine gun) .
In Blonde in Black Leather, Claudia starts out as idealistic and naive, with Monica passing for cool and street-smart (they're also dressed in the respective colors). They switch roles as the movie goes on, with Claudia becoming savvier and more down-to-earth while Monica comes off as something of a manic-depressive.
Maiko Haaaan!!! combines this with the traditional kabuki hero/villain colour schemes. The protagonist, Onizuka Kimihiko, is very excitable and is driven by his passions while the antagonist, Kiichiro Naito, is much more reserved and collected. Unless he's drunk.
The Sister Act films have an interesting example of Red Oni, Blue Oni pairs. Deloris/Sister Mary Clarence and Sister Mary Patrick are Reds. Sister Mary Lazarus and Sister Mary Robert are Blues.