This page has not yet been adopted as a policy.
The category naming conventions specify the country names to use in categories for "x of country" and "x in country" naming formats. In these categories the agreed usage is already "x of the United States".
For categories named "nationality x", a straw poll on this page has indicated a strong preference (46 out of 50 voters) for standardization of some sort with 70% (31 out of 44 voters) of those expressing a preference supporting "American x" over "United States x" or "x of the United States", with the obvious exception of proper nouns (e.g. the U.S.Army does not call itself the American Army).
Please discuss on this page's talk page.