I doubt anyone would be offended by a non-Indian wearing a sari.
I wish that were true. I asked about it on Twitter and on Facebook and immediately got a flood of responses telling me it was "cultural appropriation" and what an appalling abuse of my privilege it would be (possibly because I am not just white, but also British). I asked an Indian friend about it, and she laughed and said it wasn't a problem - in fact she would come shopping with me for something. When I mentioned that online, I was told that didn't matter, it's still cultural appropriation and therefore wrong 
That's nuts. Do they also believe when a woman of Indian heritiage puts on a pair of Levi's it is cultural appropriation? Should cowboy boots and Stetsons only be worn by American's growing up in the southwest? Should beret's only be worn by the French (well, actually I think they are the only ones that can pull off a baret, so maybe so)
There's not an Indian shop in my city that wouldn't be very happy to sell a caucasian woman a sari and they'd also spend quite a bit of time assisting with teaching you the appropriate way to wear one.
I don't know. I guess not - it's probably a race/privilege issue, i.e. I am not allowed, as a member of a privileged group, to take the clothing/customs of an oppressed one. I'm not sure though. I stopped the conversation and didn't argue back as I wasn't sure what was right or wrong and didn't want to offend anyone or appear racist.
The line of thought goes like this: you don't wear something associated with an oppressed group because often, for years, members of said group were mocked for wearing (or in some cases specifically prohibited from wearing) these items.
For a member of the privileged group to take these items and wear them purely because they like they way they look, and (because they are a member of the privileged group) not feel the weight of these concerns can feel like a slap in the face to some.
It would be, sort of like, if you had a beautiful, unique dress, that you wore often. However, every time you wear it around your cousin, she mocks you, and your dress, and says some pretty hurtful things. Then, one day, she calls you and says, "Hey, remember that dress you had? I actually really like it now! Can I wear it for a party next weekend?"
I'm not sure whether I agree with that logic, but I definitely stand by my earlier post: be aware of what you're wearing, wear it appropriately, and don't look like you are dressing up as another race.