This is really a contract that some Americans would like to impose on other Americans.
The U.S. is a free country; that's the social contract. People are free to live where they want, associate with whom they want, and speak whatever language they want. Other people are free to accomodate them to the degree they wish, or not.
But the idea that you're not "really" American unless you fit some predefined set of characteristics is just a nasty attempt to impose one set of values on everyone.