They'd probably look at you like you were an alien because most people would say either you're Icelandic or you're not. Even if you were a naturalized Icelander

They'd probably look at you like you were an alien because most people would say either you're Icelandic or you're not. Even if you were a naturalized Icelander they'd probably also say "oh but you're really American" etc if they learned you were naturalized.