The 2006 remake of The Hills Have Eyes can be interpreted as a retelling of Red Riding Hood; The family starts out as one big Red Riding Hood character who are tempted to venture (further) off the path by the 'wolf/ Garage attendant'. He sends them directly into the trap set by the other wolves(the deformed, cannibalistic desert dwellers) who 'kill granny' by taking out the car and trapping the family. The 'mutants' even have names or traits relating to dialogue from the original fairy tale - 'Goggle' uses night vision goggles to spy on the family (My, What Big Eyes you have', Lizard sniffs his fingers to get aroused when he rapes the youngest daughter(My What a Big Nose You Have) and Papa Jupiter has unusually long teeth and no lips (My What Big Teeth You Have)-he's also the only one SHOWN eating Human Flesh. He's also played by Billy Drago for maximum terror. You can take it even further by breaking down the family dynamic- The Grandparents of the family, and the oldest daughter who are the casualties of the Mutant attack are the Grandmother, the teen son, daughter and infant baby (daughter of oldest daughter) are Red Riding Hood herself: The teen daughter is young, apparently virginal but embracing her burgeoning sexuality-she's also shown to be somewhat wayward and rebellious She's also raped by one of the mutants which has got to be one of the most horrific de-flowerings ever committed to film; not to mention a helluva way to invoke the burgeoning sexuality aspects of the original fairy tale Ruby, the mutant girl who helps the victimized family, and the Geek Husband Doug, are the Axeman/Woodsman- Doug even Kills most of the mutants with a huge Axe, literally cutting his baby free of the 'belly of the beast' with the Axe while Ruby runs around the whole time in a red hoodie. It makes a decent horror film into an amazing modern fairy tale.
If a test nuke on an isolated area (actually they stayed behind) produced mutants (and I would say it was a 100% conversion rate), then the THHE universe's Japan must have hundreds of thousands if not millions of mutants. Japan was nuked twice, but there is no indication of any mutants there?
The mutations are most likely a combination of the radiation and inbreeding within the family. Not to mention that there are still babies born in Hiroshima and Nagasaki that are born with physical deformations and defects.