In our best mold, America is an idea, not a nation founded upon an ethnic identity of peoples who have been here since anyone can remember. And if you refuse to share those ideals… in Democracy, the Rule of Law, of fairness and honesty (both of which are crucial to the smooth functioning of a capitalist system, according to Friedman and Rand)… than you are denouncing your own Americaness.
In fact, it is an oath to these ideals, and to the document(s) which express them, which allows one to become an American.
America is a state of mind, shaped by the ideals of 1776 and the Enlightenment, and if you refuse to share these ideals, you refuse to be an American.