Toddlers do, and can choose one over the other without their parents or society deciding which they should like.
That statement can't be proved, and actually it's the opposite. A girl baby usually ends up with plenty of pink clothes (while still unborn), and a boy ends up with blue. Same with toys, virtually no one offers a doll to a one year old boy (while my daughter already has one and she isn't one year old yet).
So society and parents do influence toddlers.
I'm a monster
that has been experiencing with his own child, I've managed a few times to make her use some toys instead of others, just by handling some toys more than others (or playing back).
Smartphones are apparently the Best-Toy-Ever, she'd spend more time with it (turned off, and if I let her) than with toys that make noise and lights, just because she sees her parents handling it often.
