The Fawcett Society said research showed that people did not want to be "boxed in" on gender issues.
A survey of 8,000 adults for the campaign group found that almost half believed gender was more "fluid" than being confined to male and female.
Chief executive, Sam Smithers, said: "The Fawcett Society is campaigning against harmful gender norms and stereotypes which close down choices and options for children, young people and throughout our adult lives.
"When almost half of people think that we should not be confined to narrow categories of 'male' and 'female' then it's time to stop relying on outdated gender stereotypes.
"Retailers are particularly guilty of needlessly marketing products as being 'for women' or 'for men' especially children's products.
"This research shows that they need to wake up to the reality of public opinion. People do not want to be boxed in."
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