Is it possible to raise a child outside the gender binary?

A feminist couple in Sweden is attempting to raise their child (who is now two and a half years old) without gender norms. They call the child “Pop,” do not use gendered pronouns, and have kept Pop’s biological sex a secret.

“We want Pop to grow up more freely and avoid being forced into a specific gender mould from the outset,” Pop’s mother said. “It’s cruel to bring a child into the world with a blue or pink stamp on their forehead.”
The child’s parents said so long as they keep Pop’s gender a secret, he or she will be able to avoid preconceived notions of how people should be treated if male or female.
Pop’s wardrobe includes everything from dresses to trousers and Pop’s hairstyle changes on a regular basis. And Pop usually decides how Pop is going to dress on a given morning.
Although Pop knows that there are physical differences between a boy and a girl, Pop’s parents never use personal pronouns when referring to the child – they just say Pop.
“I believe that the self-confidence and personality that Pop has shaped will remain for a lifetime,” said Pop’s mother.

The article goes on to quote a biological-determinist psychologist who is dead-certain that the child’s “real” gender will assert itself sooner rather than later — and that gender will be aligned with Pop’s biological sex. While I obviously don’t share the psychologist’s strident view that gender and sex are one and the same, I do agree that Pop will probably end up identifying as either male or female shortly after Pop begins school. The gender binary is very, very culturally ingrained. When every other child in Pop’s class is a “he” or “she,” Pop will face strong social pressure to choose one or the other — no matter what Pop’s parents say about gender. It seems like even they understand this.
Given that the parents expect Pop to choose one side of the binary eventually, what’s the point of ensuring that Pop’s early years aren’t gendered? Is there research showing that those first few years are really central to forming a person’s gender identity? I guess I would love to read a more in-depth article about Pop’s family and their day-to-day.
UPDATE: Go read Holly’s take at Feministe and Helen’s post at Bird of Paradox.