I think the only country where you can truly become not-a-foreigner are the young countries (US, Canada etc) because we simply haven't been around long enough to define our national identity on ancestry. Every other country does define itself on ancestry (some more nationalistic than others).

Don't get me wrong, your presence can become very much accepted and even appreciated, but you're always wai guo ren / gai jin. I'm struggling to think of a solid example right now.

I haven't lived in Taiwan. Do they call us laowai in Taiwan or is that just a mainland thing?