We've had the cats for 3 years now, each year with a live tree. One sniffs it but otherwise leaves it be. The other one likes to bat occasionally at ornaments, but I always put soft, non breakables at the bottom for her. She honestly is more distracted by the shiny paper on packages.
Neither has figured out the tree can be a personal gymnasium. I hope to keep it that way, though one is too fat to climb in anyway. The other one cannot be left alone around ribbons- she must chew/taste/destroy. No ribbons on the tree, and the little bit of garland is high up on the tree where she won't see it. Cat is very excited for Christmas, as it means she gets scraps of paper wadded into crinkly balls to bat everywhere. I found three balls from wrapping scraps last night in various locations, including one in my work shoes.