In my (highly anecdotal, obviously) experience as An Actual Asian-American Person, the "all white people lump Asians in America together isn't that terrible" thing has never really been an issue? I mean, yeah, it's shitty when everyone assumes you're Chinese, but in practice the idea of being lumped together just becomes part of that identity. I'm half-Vietnamese and I live in Ohio, so I have had no actual encounters with people who share this heritage outside of my mother and my sister; what that's mostly led to is the Asians I have encountered all coming together over the general idea of being Asian in a place where there's not a lot of us - you know, the American part in Asian-American. The Korean woman I talk to when I go to the grocery store doesn't give a shit where my mom came from. I'm sure those sentiments exist around here, but it's by and large never been an obstacle for me, which may be very specific to the area I grew up in but who knows.
I didn't really give a shit that they had a Chinese dude playing Togusa in the movie, for example; it was just nice they had an Asian dude at all, even if I'm not sure he had more than five minutes of screentime.