Of course you can. It should happen all the time.
If, by your definition of "loyal to the United States of America", a U.S. citizen can be both loyal to the United States of America and disloyal to the Constitution of the United States of America, then your definition of "the United States of America" has a geographical basis instead of a Constitutional basis.
Take Katrina, Military enters houses and takes weapons from Constitutionally protected Citizens. That is disloyal. That is against their Oath but following policy. Black and White.
See the problem? The Citizen is correct not the Gov't.