So just to add my anecdote, I ran Conti GP4000s tires for a season once, and I had four of them all die by sidewall cuts. I spent a lot of money on tires that season. Needless to say I tried other types of tires after that. I ride all the same roads every season, and I had never had a sidewall cut on other types of tires prior to or since that one season.
So according to my anecdotal evidence, Conti GP4000s tires have sidewalls that are easily cut. I believe they are intended to be more of a racing tire than a training or general purpose road tire, so they will have more supple sidewalls that roll easier but are more susceptible to cuts.
Don't give up on Continental tires, they make a good product, you just have to find the right tire for your application. Right now I have a Conti 4-season tire on the rear and it's holding up just fine. I think I have about 800 miles on it so far this season, and I'm looking forward to actually wearing it out by the end of the year as opposed to it suffering death by glass or gravel.
-Ken