These are supposed to be progressive times for movies and people of colour. Django Unchained was a hit action movie about slavery. A black director just won the best picture Oscar for another one (Steve McQueen for 12 Years A Slave), and a Mexican won best director (Alfonso Cuarón for Gravity). Hollywood is finally starting to reflect the ethnic makeup and sensitivities of its national and global audiences.

But all those dodgy racial politics that have been swept out of live-action movies seem to have quietly found a home. Modern animation is the success story of our movie era. It pushes at the technical frontiers of film-making and gives us visual spectacles previously unimaginable, along with substantial, accessible themes. So why are its racial politics stuck in the 1970s? Maybe parents have been too busy dozing at the multiplex, or doing the washing-up while their kids are anaesthetised in front of the TV. Maybe we've dropped our guards because talking animals are the lingua franca of innocuous cuteness, but we seem to have got to a point where these movies are teaching children the finer points of racial prejudice before they've even learned to read.

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Take this week's new release, Rio 2. In terms of diversity, it's about as good as current animation gets – though that isn't saying much. It is set in an authentic foreign country (director Carlos Saldanha is Brazilian), there's a conservation-minded theme and a mixed cast of white, Latin American and African-American voice actors. In case you missed the first Rio, the story hinges around the last surviving pair of talking blue macaws: Blu (voiced by Jesse Eisenberg as a sort of avian Woody Allen) and Jewel (Anne Hathaway), an independent-minded Brazilian bird. This time round, they discover that there is a lost flock of blue macaws in the Amazon rainforest and fly there to meet them.

Rio 2 is a colourful, tuneful carnival of multiculturalism, but certain prejudices prevail. For a start, the lead characters are voiced by white Americans. Justifiable in the case of Blu, who was raised in Minnesota (having been "Americanised", he can't sing or dance like the other Brazilian birds), but more mystifying in the case of Hathaway's Jewel, supposedly born and raised in Rio. As for the couple's long-lost jungle relatives, Rio 2 uses non-white voice actors (just as James Cameron did for his blue-skinned indigenous people in Avatar). Jewel's father is Cuban-born Andy Garcia, her aunt is Puerto Rico-born Rita Moreno, her former beau is mixed-race Hawaiian Bruno Mars (there's singing involved, you see). The singing, dancing, comic-relief sidekicks are primarily voiced by African-American actors: Jamie Foxx and will.i.am as a pair of hip-hop fluent "urban" birds, and Tracy Morgan as a slobbering, dim-witted bulldog. And in time-honoured fashion, the cockatoo arch-villain of the piece (Jemaine Clement) has a British accent. Added to which, the humans we see in Rio 2 range in skin tone from pinkish to, at best, taupe, maybe coffee. Brazil's darker-skinned, African-descended contingent seem to be largely absent – this, despite a flypast of the city, sanitised favelas and all.

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Is it a coincidence that Rio 2's tacit racial hierarchy pretty much corresponds to one so often promulgated throughout movie history? It doesn't matter if they're animated jungle animals, sea creatures, fairies, cars, whatever … this same racial pyramid persists through the animated realm: white-voiced characters at the top (British just below mainstream American); other ethnicities below; darkest-skinned at the bottom. Even if the differences aren't spelt out visually, they usually are in terms of accent, which means the spectre of stereotyping is never far away. Disney's long history of racism has been well documented: the lazy, African American crows and illiterate, dark-skinned labourers in Dumbo; Sebastian, the workshy Jamaican crab in The Little Mermaid; the darker-skinned "evil" Arabs in Aladdin; the hyenas in The Lion King; the Native Americans in Peter Pan; the list goes on. Not forgetting the notorious Song of The South, Disney's 1946 musical depicting happy black slaves singing with cartoon birds on a southern plantation. The National Association for the Advancement of Coloured People (NAACP) called for a boycott of Song Of The South and issued a statement condemning the film's "dangerously glorified picture of slavery". It would be another half-century before Disney atoned with a black heroine, in 2009's The Princess And The Frog.

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But Uncle Walt's torch of bigotry still burns bright in the 21st century. Staying with good old African-American stereotypes, recent cinema has brought us such egregious examples as Transformers: Revenge Of The Fallen, in which comic-relief robots Skids and Mudflap talk about popping caps in asses, bump fists, bicker among themselves and, it turns out, can't actually read. One of them has a gold tooth. Even Jar Jar Binks would roll his eyes at that. Eddie Murphy's Donkey in the Shrek movies isn't exactly miles away from this jive-talking sidekick either. Or Chris Rock's wise-ass zebra and Jada Pinkett Smith's big-bootied hippo in the Madagascar franchise. In Madagascar 2, in a similar move to Rio 2, Rock's zebra meets other zebras for the first time, but unlike the individuated, caucasian-voiced lions they all look exactly the same.

Or how about Hispanic stereotypes? The world was furnished with one in last year's third-highest grossing movie worldwide: Despicable Me 2. Perhaps it was the hilarious Minions, but we all overlooked the fact that Despicable Me 2's villain is a grossly caricatured Mexican. Eduardo (voiced by Peruvian-American Benjamin Bratt) is fat, big-nosed, sentimental, and wears an open-necked shirt exposing a large medallion over his hairy-chest. His baddie persona is El Macho, a Mexican wrestler. And just to clear up any remaining ambiguity, Eduardo runs a Mexican restaurant. If someone was assigned to take a bunch of hackneyed tropes about Hispanic people and animate them, this is what you'd get. It's by no means the only Hispanic stereotyping out there. Try the Oscar-winning Happy Feet, for example, where the street-dancing, pleasure-seeking underclass penguins speak in Spanish accents and are voiced by … Robin Williams.

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Dr Charles Da Costa, a British lecturer who has written on racial stereotyping in animation, frames these portrayals within the context of what he calls "PEPs": Problem Contexts, Entertainment Contexts and Performance Contexts. "Within PEPs, black people and other genotypes have to be associated with vexing circumstances," he says. "Strive to pacify, make others happy and be exceptional or extraordinary – far from 'normal'. Villainy, exoticism, jocularity and athleticism are common indicators of this malaise. Images of ethnicity do not need to be conveyed within the narrow scope of PEPs."

The slow, expensive, labour-intensive process of producing animation could also be a factor, suggests Da Costa. "Decisions on character and performance must be made quickly in order for design and production processes to commence and advance. So regarding representations of ethnicity and epidermal type, family animation often finds itself in a bind. It consciously and subconsciously weighs financial against moral obligations, then unconsciously opts for the 'safe' representational defaults – stereotypes."

There's possibly another imperative here. In today's global cinema market, movies such as Rio and Despicable Me 2 can expect to make twice as much overseas as they do in the US. So there's the desire to be slightly more outward-looking, but not to the extent that domestic white audiences are turned off. In the same way African-Americans once cheered Mammy in Gone With The Wind – not because she wasn't a racist portrayal but because she was an actual black person with a speaking role in a Hollywood movie – so non-white audiences are assumed to be grateful for whatever representation they get.

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Put all this together and what you often get is an apparently globalised story peddling lowest-common-denominator racial shorthand. It could look like Disney's Planes – a spinoff of its equally shallow Cars movies – which follows a round-the-world race between anthropomorphised vehicles. The premise makes for kid-friendly, merchandise-shifting action, while the international scope affords the chance to visit key movie territories (India, China, Germany) and stuff the cast with international cliches. There are vehicles wearing straw hats toiling the paddy fields in Asia, for example. There's an emotionally repressed British plane (voiced by John Cleese), a seductive but mendacious Indian plane (Bollywood star Priyanka Chopra), a dainty pink French-Canadian female plane, and no surprises for guessing that the Mexican plane is rotund, sentimental, romantic and wears a wrestler's mask. They could have called it Around The World In 80 Cliches. As Variety reviewer Justin Chang put it: "Planes is so overrun with broad cultural stereotypes that it should come with free ethnic-sensitivity training for especially impressionable kids."

Like many animated stories, Planes hinges on the premise of an exceptional individual who dreams of transcending their allotted role in life – in this case, an ambitious crop duster (voiced by Dane Cook). The other planes ultimately help him by donating parts. It's the same story in Turbo. Ryan Reynolds' snail also harbours racing ambitions, and is aided by street-talking comic-relief sidekicks voiced by Samuel L Jackson, Snoop Dogg and Michelle Rodriguez, among others. And let's not forget Turbo's human accomplices: some Mexicans who run a taco stand and The Hangover's Ken Jeong as a Vietnamese woman. Social mobility is only available to white characters, the message seems to be, and it's the job of non-whites to facilitate it.

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As if it couldn't get worse, recent animations have hit upon a new way to circumvent this problem: get rid of people of colour altogether! Which brings us to Disney's latest smash-hit Oscar-winnig animation, Frozen. Frozen was applauded for its nuanced, active female characters (let's gloss over the Barbie-like approach to body image for now) in contrast to passive princesses past. On a diversity level, though, the film's vision of wintry unmitigated whiteness extended not only to the landscape but the movie's characters, too. "Aha!" its defenders could say. "This is a story set in 17th-century northern Europe, why should there be any people of colour?" To which the reply could be: "This is a work of fantasy concocted in ethnically diverse, 21st-century America, in which you have chosen not to cast or represent a single non-caucasian person."

For campaigners such as the NAACP, Frozen represents a step backwards, says Robin Harrison, of its Hollywood Bureau. "It was just a few short years ago that we were finally introduced to the first African-American Disney Princess, Tiana, portrayed by Anika Noni Rose," she says. "We had hoped this was a turning point for the industry. Unfortunately, what has now become the most successfully animated feature of all time, Frozen, is probably the least diverse. There is still much work to be done in all areas of film and television animation created for children and adults."

Look around and you'll find other animated stories set in these ethnically cleansed "historical" realms, such as Robert Zemeckis's weird, motion-capture rendition of Beowulf. Or the very likable How To Train Your Dragon, whose Viking-ish setting also justified an Anglo-Saxon voice cast (at least the movie's theme was insular people confronting their prejudices). Or prehistoric adventure The Croods – a white-voiced family in a time before race even existed. Then there was Pixar's Brave, set in an ancient Scotland chock-full of fair, flame-haired maidens and fiery ginger warriors. No need to stray beyond the stereotypes, no need for people of colour.

Talking of Pixar – and we need to – its record on ethnic representation during their vaunted "golden age" demands another look. Let's see, there was Samuel L Jackson's Frozone in The Incredibles, Jordan Nagai's Vietnamese kid in Up, Delroy Lindo voiced a dog in Up, and, er, that's right: the pioneers of 21st-century animation have taken us through worlds populated by toys, monsters, insects, sea creatures, superheroes, rats, French people and robots, and barely found a role for a non-white actor in any of them. The closest Pixar have come to representing ethnic diversity, in fact, was the spaceship towards the end of Wall-E: a post-apocalyptic world of obese, cosseted, unthinking, conformist consumers who were too busy looking at screens and slurping from cups to actually notice their dystopian reality. At last, a rainbow nation Pixar can get behind.

Clearly, none of this has been a barrier to success for the animation sector. Nor should it take away from these movies' many strengths. And it would be absurd to argue for tokenism, or quotas, or strict guidelines on what ethnicity of actor is entitled to play which species of animal. But surely it doesn't have to be like this? Plenty of movies manage to get it right, or at least less wrong. The biggest movie this year so far, The Lego Movie, felt no need to caricature along simplistic race lines. Last year's Epic included Beyoncé as a brown-skinned fairy queen (and, oddly, rapper Pitbull as a ghetto-pimp toad). Lilo and Stitch was a Disney high point. And even a movie such as Madagascar 3, which threw together a United Nations of funny-accented talking creatures, got away with it by making them more nuanced and eccentric than standard caricatures (and being hilarious).

Perhaps it's a matter for the film classification boards. They could put a warning on the certificate: "Contains mild fantasy violence, very mild language, a white-supremacist subtext, and grotesquely derogatory portrayals of ethnic minorities." Or: "Probably won't make your child into a racist, but sure as hell ain't gonna help." It's not as if children have demanded any of this, but they are the ones soaking it all in. It goes without saying that racism is learned, and how diversity is portrayed on screen is a big part of that learning process. One day, our children could look back on these movies in the same way that we see Song of the South, and wonder why their parents did so little about an iniquity that was staring them in the face.

• This article was amended on 9 April 2014. The original incorrectly stated that Planes was a Disney/Pixar film. It is a Disney film, but not a Pixar production.