In fact, the United States recognizes the Vatican as a city state, established by the Lateran Treaty (1929). Italy's anti-Jewish laws of 1938 prohibited marriages between Jews and non-Jews, including Catholics. The Vatican viewed this as a violation of a concordat between Italy and the Vatican, which gave the Church the sole right to regulate marriages involving Catholics. [Wikipedia]
Government may not influence the Catholic Church. On the other hand, the Church may influence government at will, and ought to, especially on morals. American Catholics like me have no interest in a theocracy but deeply desire that a Catholic culture suffuse every street. Truth is irresistible.