I haven't had a problem's with my two yet at all. We have a fake tree with lights and ornaments and they have never even bothered with it. I think they barked at it the first day like "why is that big thing in my family room" but nothing after that! We don't use tinsel so that was never an issue.
We only turn the tree lights on when we are home and in the room, plus they are pretty much never unsupervised.
We do have stockings for both that hang on our fireplace with there names monogramed on them. Really cute! I had them made by "Personal Creations" as well as my husbands and mine!