We don't put up a tree for just the two of us anymore, but when we did and in my previous lifetime, our cats have always wanted to explore the tree. Cats are natural tree climbers, so of course they want to climb the tree. Good thing we didn't have a "Christmas fire plug" because we had a dog, too. Anyway, when the kids were small, we had a green artificial pine tree the kids dubbed "the green commode brush". Each branch had to be inserted individually (what a pain!), and after a couple of years we had to replace the tree because the weight of the cat on those branches completely stretched out the holes and the branches would fall out.
Cats love the tinsel and the movement of the ornaments on the tree, especially if they are shiny. Christmas bows on packages are as tempting as shoelaces, and angels are to exercise their little sharp teeth on. Just be sure they aren't plugged in or your kitten may get a shocking experience.