Born the USA, I have no accent. However, it is amazing how many people simply assumed that I must have just gotten off the boat, or am somehow less American.
But I never found somebody's mistaken assumptions about me offensive. Probably because they mean no malice and end up feeling a lot worse about it than me.
But the "ching-chong" sort of deal does conjure up all the nerdy Asians that appear in liberal Hollywood films that features an Asian male that isn't a martial artist or a gangster. When popular culture tends to have an overwhelmingly negative portrayal, you tend to be a little hypersensitive about it.
You are an American, you know that every ethnic group has at one time or another been, either the idiot or the villain in the public media, especially Hollywood. The Irish were considered trash, the Germans were spies and worse, Italians were Mafia, white Southerners are rednecks, etc. In the scheme of things Hollywood has treated Asians pretty well. As a child, I loved western movies and the orientals were portrayed as gentle, hard working, people.
You don't see the Irish running around like hypersensitive pussies every time someone tells them to stop chasing their Lucky Charms.
Stop being a pussy.