The simple answer is no - protein will not cause liver damage. At least it will definitely not cause liver damage when taken in moderation in accordance with the needs of your body. Back in the days some people would say that because of all the additives in the protein products and the extreme dosages people would take. Obviously, your entire body will struggle with protein if you take too much of it, be it from a protein shake, or from natural food sources. Therefore, just take as much as you need - no more, no less, and there will be no damage whatsoever.