Sexism and stereotypes happen by osmosis, you have to be really resilient to fight it. We don't eradicate it here, but we do offer an alternative. Today is 'dress up pirate day at school', my dd is five and, so I'm told, striking and beautiful. She wore Jack sparrow dressing up outfit, unlike every other girl (bar the one they call a 'tomboy') who were Pirate Princesses. It was a really proud moment, not only is she bucking the trend but she did it without thought. Everywhere, and I do mean everywhere, people ask her name and tell her she's beautiful, little else, my boys are beuatiful too, but people barely pass comment on this, comparatively, and it certainly isn't the only thing they say.
At 2-3.5yrs old dd would wear no other colour but pink, without a huge fight, and for the whole of '3' she would not wear shorts or trousers without a fight.
She wants to be a doctor when she grows up, her room is pink, she does not have a Barbie, she does have baby dolls, a kitchen, ironing board (all wooden but a bit pink). She loves being a girl but as yet is not limited by this.
Every time one of my children defines colours/objects as for girls or boys they are corrected. My ten yr old is alone in his class with this sort of thinking, I think it's tough to be a boy that thinks of girls as equal...ds2 is matter of fact about feminism, he thinks it's a given!
We do talk a lot about image, the right thing to do, sexism etc. I find an open and constant dialogue makes stuff normal.