Labour MP Jacinda Ardern has written to the Human Rights Commission calling for an investigation following Herald on Sunday revelations this month.
"The company's 'catch-all policy' is unfair and unjust. If it were applied to any other workplace we would find many employees would not meet such a test."
Green Party disability issues spokeswoman, Mojo Mathers, said Restaurant Brands' policy was discriminatory.
"They exclude from employment many disabled people who may have a lot to contribute to the workforce but cannot tick all the boxes for the skills. I will be pursuing it."
Restaurant Brands chief executive Russel Creedy said the company had offered support for those who needed to be moved into other jobs or activities. "We have not made changes to our employment policy but disestablished limited duties roles."
After 18 years' service - no job
Bob Van Lunenburg broke into tears when KFC put off his intellectually-disabled daughter after nearly 18 years on the job.
Van Lunenburg, 83, says Tanya was fired from KFC in Birkenhead where she'd worked two afternoons a week packing potato and gravy.
"That was her whole life and it gave her something to look forward to," he said. A KFC outlet management told him Tanya, 48, could not help at the front counter and so her job had been discontinued.
"I went outside and cried."
He says a subsequent mediation meeting was unsuccessful. "I told them, how you could ever do that to a girl like Tanya is beyond all belief."
Van Lunenburg had a sleepless night churning over what he "should have said".
"I thought if only I'd said more, I might have been able to help her keep her job."
Tanya's sister Nikki says her sibling loved putting her uniform on and was proud of her job. "For her it was very significant."