Mine's a daily driver. I take it everywhere. Grocery shopping, work, errands, etc. It's a car. I use it as such.
If the top is down while I'm driving, I'd leave it down when I park. Pretty much anywhere. With the red clip. Not that the top would be up if I didn't have the red clip. I'd probably leave it down regardless.
My biggest concern about parking somewhere with the top down isn't someone doing something malicious to my car. My biggest concern is coming back and finding bird crap on my interior!