IMO it is overprotective.
I took my first out to the shops as soon as I was out if hospital. She was 2 days old.
My son was only 3 days old when he went to the daycare centre where my eldest daughter went and all the kids were hovering around.
I am maybe a bit too relaxed with my newborns but I would be bored sh1tless staying in the house all day for more than one day.