I think my wife is too obsessed with hygiene and is overprotective of our daughter. How do I tell her to be more carefree?

It's mother only who can be more careful about hygiene & protectiveness for her child. Too much carefulness is not a bad thoughts. It teaches a child how to well behave and well live in the society. You should have discussion with your wife in a positive manner that we should exclude same area's where child does not like the hygieneness. You both need to observe the child protectiveness at his/her own strengths and have some extra curricular activities for the same.