“The embassy isn’t to the Church per se but to the Vatican City State, which is all that is left of the Papal States—109 acres that are a sovereign nation, and not part of Italy. It is much diminished, but the nation has existed in one way or another for 1257 years (see my post 35 above). If the head of another denomination also happened to be head of a state, it would make sense to have an ambassador to that state.”
Fictional non-rational excuses. Fictional in how the tiny remnant of land comprising Vatican City because of the deal the Italian government made with the Roman Catholic Church, and leaving scrap of sovereignty to that tiny spot of land is not - at this point in civilized history - a rational reason for an American embassy there and that is in fact ONLY an excuse, and NOT a cause or a reason. IT IS IN FACT an embassy to the Roman Catholic Church, and it should not be so, as we have no “embassy” to any other Church denomination. I am not being “discriminatory” to Roman Catholics in saying that. It is being “discriminatory” to all other faiths and Churches to have an American embassy to Roman Catholics.
We have a number of ambassadors to governments whose heads of State are also the heads of Churches. Queen Elizabeth is the head of not one, but two Churches, and the head of a good number of governments. Xi Jinping is not only General Secretary of the Chinese Government, but also in the end the head of (among many other religious organizations) the Patriotic Catholic Church.
Pope Francis is ranked among the most influential leaders in the world—the Pope generally is in the top 10— http://www.freerepublic.com/focus/f-religion/3086087/posts
(Pope Francis was ranked fourth this year, up one spot from Pope Benedict the year before.)
Twitter finds Pope Francis most influential. http://www.christophersmith-op.com/2013/11/04/twitter-study-finds-president-obama-is-least-connected-and-pope-francis-is-most-influential/
Granted the significance is primarily because of spiritual power—but it is not to be underestimated.
The “deal that the Italian government made” and the status in which the Holy See is held is sufficient for about 180 governments to have embassies.
If there are other denominations that have a leader who is a sovereign and who is as influential, we would be discriminating if we were ignoring them. Otherwise, you are comparing apples and oranges.