The Holy See is the government of the Roman Catholic Church, also governed by the pope as a theocracy with an appointed administrative apparatus. The Holy See credentials ambassadors and maintains diplomatic relations with other states. The Holy See has a secretariat of state, which because of its importance is the only secretariat located within Vatican City, lesser bureaucracies being located elsewhere in Rome. The Holy See is a member of international political organizations, for example, the International Atomic Energy Agency, and the United Nations (nonvoting, by its choice). The Holy See's operating income derives primarily from extensive real estate holdings. In 2006, it had revenues of $310 million, $101 million derived from the international "Peter's Pence" levy, of which 28% comes from the United States.
In short, Vatican City is a territory created to serve a single religion and the Holy See is its governing theocracy. The United States recognizes Vatican City as a sovereign nation, and maintains diplomatic relations with the Holy See. This has not always been the case. Vatican City was established in 1929, and the US had no formal diplomatic relations with the Holy See from 1870 until 1984. The current US Ambassador's office is in Rome, while the current apostolic nuncio has an office in Washington D.C.
With this in mind, it is beyond dispute that Roman Catholic Church is not merely a religion with an interesting tourist destination — it is also a foreign government that advances a political agenda.
Among the political issues that the Roman Catholic Church advances are the impermissibility of abortion, and the legal subordination of sexual minorities. By its own moral reasoning and through its Canon Law, the RCC rejects abortion and gay rights. However, if it were purely religious interests served by those doctrines, the Church would make those arguments from the pulpit and bind only Catholics to them. That is not the case. The RCC reliably lobbies for legislation that supports their political agenda at a federal, state, and local level. The RCC also reliably files amicus curiae to insert its political opinion in court cases where the legal rights of sexual minorities are at stake.
One might ask, how does the issue of whether the federal government may fire a federal employee for being gay at home have anything to do with the deposit of faith or other workings of the Church? Obviously, it doesn't. It has everything to do with the Vatican's desire to impose its politics on other governments. They did it very effectively for centuries. It's clearly a hard habit to break.
Sure, they aren't the kingmakers they used to be, but still — it's unwise to underestimate the power of Vatican politics. Somewhere between 20% and 39% of Americans were baptized Catholic. (Naturally, that doesn't mean they're practicing Catholics, or even particularly devout Catholics, but Catholicism, like Judaism, is an identity even among the wayward.) Regardless, the current Supreme Court is 56% Catholic. If Sotomayor is confirmed, it will become 67% Catholic. That's an impressive accomplishment for any minority group. I suspect that it is their reliable anti-abortion stance that has historically assisted Catholics in filling so many federal bench appointments. Hell, the percentages wouldn't particularly bother me except that the Catholic justices have shown such enthusiasm for ruling in ways that are clearly informed by the teachings of their faith over the terms and principles of the Constitution, the law, or the interests of justice.
Anyway, can we just quit pretending that one's identity and background don't inform one's decision-making, or if they do, that's always improper or off-limits? The fact that identity and background are relevant to deciding cases is precisely the reason why trial judges preside over hours and hours of voir dire where prospective jurors are questioned about their identities and backgrounds. The dirty little secret of voir dire? Jurors aren't questioned to exclude those who are biased — they're questioned to ensure that the panel is biased favorably.
So as to the SCOTUS nomination, I have no problem with interrogating a Catholic judicial nominee regarding his or her view of the RCC's penchant for church-state entanglements, his or her view of the Church's intervention in the American political process, and how he or she might address threats of excommunication based on a legal act or statement, etc.
That's not a religious test, it's a reasonable and sensible inquiry into how the nominee regards the interference of a foreign government, or whether a Catholic nominee is even capable of viewing his or her Church that way.