Will every hairy baby grow up to be a hairy man?

No. Hairy babies often are covered in a type of hair called lanugo. This usually falls out in weeks to months. When a baby comes from a hairy mom and a hairy dad, that baby is likely to grow up to be hairy, whether male or female. Conversely hairless parents rarely produce very hairy children. And in response to your question; not if they're girls.