Another girl who was also wearing leggings was allowed to board the flight from Denver International Airport to Minneapolis after she changed, a witness said.
A United spokesman Jonathan Guerin told the New York Times that the two girls barred from flying "made an adjustment" to their clothing and were waiting for the next flight to Minneapolis. He did not know whether they made it aboard.
The incident was reported on Twitter by Shannon Watts -- founder of gun reform group Moms Demand Action -- who was a passenger at the airport waiting to board another flight to Mexico.
"She's forcing them to change or put dresses on over leggings or they can't board," she said. "Since when does @united police women's clothing?"
"A 10-year-old girl in gray leggings," she added of one of the girls. "She looked normal and appropriate."
With that, the charges began to fly across the Twittersphere, with outraged travelers and celebrities weighing in with accusations of sexism and corporate ham-handedness.
"I have flown united before with literally no pants on. Just a top as a dress," declared model Chrissy Teigen in one tweet. "Next time I will wear only jeans and a scarf."