Hi Nancy,
I think what you are referring to is admiration and appreciating elements of someone else's heritage. However, cultural appropriation is taking a culture's identity, for lack of a better word, and claiming it as your own, as in Rachel Dolezal's case. She took her admiration of black culture to an extreme by identifying as black and denying her own race.
There is a difference between the two concepts and people are offended by the latter.