<ahem> Italian Christian Democrat Party</ahem>
Um, I apologize in advance if this is a hijack, but in the UK, a “public” school is what Americans call a “private” school. This site offers a good explanation. So a public school run by the Catholic Church would not be a good example of the OP’s premise.
>practically speaking being an attending member of a religion (and one religion in particular) appears to be almost a pre-requisite for election to government.
Err, unlike which countries? Every country has a dominant religion. How many Islamic presidents has Argentina had? How many Jewish presidents has Russia had? How many Buddhist presidents has Iran had? How many atheist presidents has Australia had?
While its “cool” to bash the US on all things on the web, I think its an unfair characterization. The US, unlike a lot of European and Asian countries, was founded as a secular country, which is almost unheard of. Yes, there’s a fair bit of religiosity, but calling it a de facto theocracy is ridiculous.
That’s not exactly right, and besides Ireland is not part of the UK. The term “private school” is used in the UK. Public schools are a subset of private schools. They are the old, prestigious private schools that date back to the time before state-funded universal education. They may originally have been run on a chartiable basis, but they now charge fees, and very expensive fees too.
Not exactly “unheard of.” Wikipedia has a long list of states that are officially secular.
American Taliban The American Taliban
It should be noted that while most schools in the Republic Of Ireland are run by the Catholic Church that many of these schools have non-Catholic students and the issue of ones religion arises mainly where there is a scarcity of places in the school. There is also a significant non-denomational movement, the Educate Together Schools and a plethora of religious but not Catholic schools.
To my mind, Ireland probably used to be a form of theocracy, but has ceased to be in recent years. Divorce is legal, support for legalising abortion is high, the church by and large does not get to determine the national political or cultural agenda in the ways it did in the past.
Oops. Sorry. Ignorance spanked!
I also think the biggest marker for unofficial theocratic tendancies is the non legalization of abortion. Its illegal almost all of the cases for religious reasons or by religious lobbying, especially Catholic.
The Church of England. 
C of E vicars, rectors, deacons, bishops, archbishops and so on are all paid a weekly stipend (effectively, their salary) by Her Majesty’s Government. I think that counts as state sponsorship, don’t you?
It’s not quite that simple- the Sovereign’s coronation vows include one to defend the Church of England. The office of Supreme Governor/Defender of the Faith isn’t something separate and apart from the office of monarch.
Really Not All That Bright: Check my post again. I was asking what the established relgion in the United States would be.
Out of curiosity, though, does the salary for the Church of England personnel come from the government or from the parishioners?
Not true!
The Church of England, although an established church, does not receive any direct government support. Donations comprise its largest source of income, though it also relies heavily on the income from its various historic endowments. As of 2005, the Church of England had estimated total outgoings of around £900 million.[20]
Wikipedia Article
That income is used to pay the stipends.
Not to mention Germany - the largest party there is the Christian Democratic Union which is currently in power.
Ah. So you were.
I stand corrected. However, those grants of land and stocks and the like that make up its endowments (but have presumably been shifted into more modern investments these days) did originally come from the Crown, for the most part, didn’t they?
Well, for the most part they came from Bequests, left in the Estate.
I am by no means an expert on the subject, and I suspect the situation is rather similar to the powers of the monarchy, in that they have alot of power on paper, but if they ever tried to use it there would be public uproar, and would lose it sharpish. On paper at least, I think the church of England is the “established religion” of the realm so all English citizens are considered members of the church of england, legally speaking.
Additionally I think the “Peculiar Courts” are part of the Church of England that still have power over all members of the community in secular matters.
If anyone (unlike myself) actually is an expert of this kind of thing I’d be interested to have a definitive answer.
So the head of the secular government is also the head of the state religion. That pretty much defines theocracy.
Well, it’s not like she actually has any real power in either sphere.
No, but the head of government (ie., the PM) is responsible for [del]appointing bishops[/del] recommending canons for appointment by the Queen, and he does have real power.
Quite which is exactly my point, on paper the UK is a theocracy, and the US is avowedly secular. In reality the UK is avowedly secular, and the US is much closer to being a theocracy that any other western country.