Anything with your ID info can be a starting point for someone trying to steal your identity. However, the typical insurance card doesn't have much.
I work in a related field and know a little about this stuff. True ID theft, although potentially a never ending nightmare, is more rare to some degree than the news media portrays. What is more common, and often labeled ID theft, is getting your credit card compromised (people getting your number and going on a shopping spree). This is a hassle, but usually doesn't leave you out of much money, if any. With all that said, I shred everything with my name on it and I keep track of my credit report.
I do worry about the possibility of my truck getting broken into or stolen. I keep my registration and insurance info in my 4th gen's "hidden glove box compartment". Unless you're looking for it, it's tough to find.