Opposing the binary genders

Strictly speaking for myself, growing up I was taught that there were only 2 genders: Male and Female.
Yet in my GWS class a topic was recently brought up, what if we reject the binary genders that are defined for us. In our modern culture it is becoming more and more common for people to be "transgendered" or even "Intersex" for those of you who don't know an intersex baby is that of which is born with both sets of genitalia.

The question arose if you were the parent of an intersex baby would you choose which organ your child kept and raise it as that gender or would you let it grow and choose which it felt as it should identify as?

At what age is it appropriate to let your child decide how they identify? When are they old enough to know whether they are a boy or a girl... more importantly how do you raise your kid allowing them to choose but explain that they will be constantly outcasted.

Gender separation starts at a young age. In preschool we separate to boys bathrooms and girls bathrooms or we play in our separate groups. Girls typically with dolls since that's most likely what they have at home and boys with trucks and cars. How is it that as a parent you could allow your child to grow up confused and ridiculed practically forced into making a gender decision based on society itself.

I know personally that if I hadn't been called a girl or been raised knowing I was a girl, I would probably have identified more with the male side of things: blue was my favorite color, and I wore pants instead of skirts or dresses all of these seeming to be defining factors of how we recognize boys or girls.

There was an interesting case of which parents had decided to have their newborn son circumcised and something went dramatically wrong, it was then as a result decided that the best course of action was to mutilate the rest of the male genitalia and give the child female parts to raise it as a girl.
The problem with this being that the chemical balance in the brain is difference between males and females and that simply giving him a doll and growing out his hair using female pronouns will not make him a girl.
The amount of flaws within our society, which is just now beginning the process of rejecting the binary system, is monumental. Which is why it is more so up to parents to educate their children and to decide if they want their children to decide who they are, which ultimately they will do anyway.