I think gender neutral toys are a marketing gimmick and don't matter. Hear me out.
When I had my first, a son, I was in a playgroup in a very liberal, educationally focused neighborhood. My playgroup had mothers that only bought gender neutral toys, others that made sure their boys had (correctly gendered) baby dolls and their girls had trucks. Honestly, I was kind of a slacker and didn't care. My son had tons of stuffed animals that he loved, but he had no interest in baby dolls and before 12 months showed in interest in all things with wheels, motors and building. He was all boy all the time.
My daughter was born into a boy house lacking all things pink and girlie. That did not stop her from being drawn to any and all things pink. When she was 10 months old we took her to get her first shoes. They had no "girl" shoes in her size so I put a brown boys' gym shoe on her. Honestly they were super cute, not boyish and I would have worn them if they were in my size. She picked up her pink Robeez and started crying "No, No," as she tried to shove her pink shoe over the brown one. But for all her love for pink and babies, her desire to be like her brother was stronger. She quickly abandoned her "girl" toys to go build with him or race cars.
There are four years between my two girls. When PBbaby was born, she was born into a house full of toys - girls', boys', neutral, pink, blue, anything you could imagine. Other than a recent attraction to Thomas, this little girl has wanted only to play with babies, princesses, and tea sets. She has zero interest in cars or motors. The only thing she has ever done with blocks is knock down what her siblings make. She is all girl, all nurturing all the time.
My youngest is only 7 months so he's just starting to play and his preference is: What do you have? Give it to me! He will turn his head if he hears a motor from a car or plane, but he will also go out of his way to try to take the girls' baby dolls. See it's not the toy that matters, it's the person that's holding it. It's not the color but who they are emulating and want to be like.
Do parents influence that? Sure. My husband loves cars, trucks, planes, all things with motors. Did that natural desire influence our son to be so boyish? Of course! He wants to be just like dad! I don't doubt, though, that if he had a strong desire to be just like mom, he would. My daughters may love to play with dolls and wear head to toe pink but they are also super athletes who love to wrestle and rough house.
Their toys have nothing to do with who they are and as parents we probably need to stop overthinking it and just let the kids play.
Melissa is mom to 4 kids and 2 angels. She chronicles the sticky bits of motherhood at Peanut Butter in my Hair.
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