Actually, we have had fewer problems with appearance than we have had with the concept of adoption. However, in any case a great deal depends on the parent’s approach as well as the child’s personality. We tend to turn things like that into a joke and a learning opportunity both.
My husband (who is of Japanese ancestry) tends to tell folks who ask where he is from that he comes from 1) Chicago (where he grew up), 2) California (where he was born), 3) a concentration camp (he was born in one of the WWII internment camps), or 4) America. OTOH, he sometimes has to deal with people who will walk up to him and insist he is Inuit, or ask him what tribe he is from, or will insist on speaking Spanish to him (I am the Hispanic one in the household).
Our kids have a problem in that they are both mixed race but my son definitely looks African-American, while my daughter, with similar features, is blond haired and green eyed with pale skin. Many folks assume that one is adopted but the other is not. The answer they learned to give is that everyone is adopted at our house, even the dogs, and that we specialize in looking different from each other so we can tell ourselves apart.
In any case, we have had relatively few problems because we make light of any problems we have come across, we are obviously and publicly proud of our diversity, and possibly because we greet each new person as an individual greeting another individual and take their questions at face value. No looking for motives here!