This is an interesting question, Peri, and something I think about a lot.
No, I do not feel offended if I see someone else (Asian or otherwise) wearing Asian-inspired clothing (so long as it does not promote racial stereotypes of course). It's obvious to me that the designs, styles, and patterns are being used as fashion.
What does seem a bit costumey and maybe sometimes suspect to me is if someone is wearing an entire ensemble of traditional ethnic clothing. Such outfits generally denote membership in a particular group, whether it be cultural, religious, or otherwise, and seeing someone who is obviously not a member of that group wearing them is a bit odd. It's particular strange when it's something like a full ceremonial kimono (with the obi belt and sandals etc) because this is not something that regular Japanese people wear on a daily basis anyway. It is ceremonial and special and worn only for special occasions with specific cultural signifiers, so it might even be considered offensive to wear something like that without understanding the cultural implications.
Of course environmental norms play a part here too. I remember a (American, Caucasian) friend who had spent time in India telling me that she now (in the US) only wears her salwar kameezes at home because she feels uncomfortable, as a white woman, wearing them out of the house in the US. However, she said that in India, everyone, Indian and foreign, wore them out and about so it was perfectly normal there and did not have the cultural signifiers that it has here.
Would I personally wear a kimono jacket? Probably yes, if I found one I liked. But I would actually prefer to wear one that is fashion-y rather than super traditionally styled (for example, with trendy elements like a high-low hem or something) because I don't want to look like I either am or are pretending to be part of a particular cultural group (Japanese) to which I do not belong but to which I could conceivably belong based on my looks (I am actually Chinese). ETA: I would not wear it with any other Asian-inspired items.
