Do you put top up when parking at the grocery store, etc?

[Jamesp]

Many years ago I had a shiny new 300Z and saw a jerk push a shopping cart at the car, he looked up from the cart, saw me and chased the cart down before it hit the car. He didn't look like he had, or ever would have a nice shiny car and apparently figured no one else should either. He just turned and slunk away.
I would keep the top down just about anywhere with nothing in the car to steal, but I installed one of Fred's wind breakers in it, and since it says "PORSCHE" on it (and lights up!) I'm sure some fine gentleman would come long to remove it from the car for me. The top goes back up for the most part.