Women don't get mistaken for men, nor men for women (except by people who aren't really looking - the same people who think 5ft 1 mum = teen mum without taking in grey hairs, wrinkles, bifocals 
...) , because they've been through puberty so are different in every way from skeletal structure to muscle and fat distribution to facial hair or lack of to voice - so they're different face and body shape, different skin, different everything. Socialisation combined with body shape even means they stand differently.
Girl and boy 3 year olds look the same. Interestingly one poster claims her DD was girl shape as a baby because she was fatter and another that her DS was boy shape because he was "a great lump" - 
It doesn't matter at all that a 3 year old girl with short hair and a 3 year old boy with long hair might be assumed to be a long haired girl and a short haired boy.
It's not a reason to cut or not cut hair.
Really nobody should care as long as the child themselves knows what their sex is, because it's part of knowing who they are and later knowing what to expect from puberty etc etc. Obviously anyone who knows them will know because of their name and because the child know and for safeguarding and because it is just a general fact about them etc etc. It totally does not matter to strangers in the supermarket/ playground whether a 3 year old is a boy or a girl. The sexes do look the same in clothes when under 8 or 9 unless you mark them using clothing or hair and that's fine.
My youngest son had beautiful long blond hair until he started preschool. I left it long because he was the first of my kids to have anything in the way of hair by 2! My older kids had whispy baby hair for years. His thick, fast growing, blond mane was a revelation and when ds1, then 5, asked him if he wanted his hair like ds1s he said no, [name of ds1] had [name of ds1] hair and [name of ds1] had [name of ds1] hair.
When he started preschool he got a few comments but was much admired and told he was a surfer dude mostly, but then one day of all people the dentist who went into preschool to do a little talk for the children on brushing teeth called ds2 forward to hold an oversized toothbrush prop and called him a beautiful little princess - and would not be corrected when ds2 said that he was a boy.
After that he wanted "boy hair" and we took him to the hairdresser.
It was a sad way to see it go.
People are arses.
But that doesn't change the fact that you can't tell whether 3 year olds are boys or girls if they're dressed unless they're marked as such with clothing or hair, no matter how much some parents believe their baby is has a post pubescent male musculature or has feminine curves 