"no offense" doesn't mean that they think you're not american, even though it could mean that, similar to "where are you from". I'll grant you tv/movies, though that is undeniably getting better. I grew up in a town literally called "white settlement", conservative suburban but semi rural texas, most of my friends were asian and while I don't think they NEVER heard the word chink, it was never in a threatening or even (as far as I observed) bullying (i.e. directed at them) way - alot of the kids in public school have an EXTREMELY rough way of speaking (they're barely able to communicate without expletives). All that said, there's some things you didn't mention - a lot (but not all) of my asian dude friends had a bad time with dating for instance, and sometimes some of the teachers would be unable to tell them apart, etc..