Should we be saying "America is....." any of these things? One can--it would be advisable to be correct and accurate in your depiction (which eliminates the assertion of America being a "white" nation).
Should the President of the United States be making such statements (especially the current one, who claims some expertise on the Constitution) and not distinguishing between our government and our society? Absolutely not. Broadly, America is a Christian nation, but from the start has been a nation without Christian government, and which has at the very core of its law proscribed Christian government; that is the statement the President of the United States should be making, if he wishes to fairly and accurately depict the demographic and legal reality that is America.