Living in Israel for eight months, even as a student in an almost-entirely English-speaking environment, made me feel very American.1 One of the features of Israeli political culture that caught my eye was that in Israel, the state serves to allocate privileges and duties among groups, and not just among individuals.
The Israeli educational system illustrates the phenomenon. There are not only separate public school systems for Jews and Arabs, but separate systems for secular and Orthodox Jews. Haredi families who consider the state religious schools to be too left-wing can send their children to schools in the Chinuch Atzmai system, which is not run by the Ministry of Education but receives heavy subsidies from the state.
Israel is a peculiar country, especially when it comes to religion/state relationships, but when it comes to state-sponsored religious education, among developed Western2 nations, the United States is the real outlier. In Germany, Catholic, Protestant, and Jewish religious education is provided through the public schools at state expense. In Great Britain, daily worship is mandatory (although, apparently, it is often pro-forma) and religious education is part of the standard syllabus; furthermore, parents may send their children to faith schools that are run by religious bodies, funded by local governments, and regulated by the national government. In some Canadian provinces, Catholics or Protestants can form parallel school systems in areas where they are religious minorities, and other systems for subsidizing religious education exist, depending on the province. Turkey has vocational high schools that train students to become state-employed imams.
The Religious Right in America hopes some day to reverse Supreme Court decisions that shut down religious observance in the public schools, but as far as I can tell, they do not hope to reproduce the Israeli or German system in America: that is, they do not want a multi-confessional school district to set up separate classes or parallel school systems for Baptists, Pentecostalists, and Catholics. They simply want school boards to have the same constitutional power to establish a school-prayer text as they currently have to schedule football games. In recent years, some conservatives and libertarians have taken a different approach, advocating for school vouchers. But here, the emphasis is on empowering individual families to choose a school for their children, not on empowering religious bodies to establish schools where those children might attend.
The American separation of church and state can also be contrasted with the French practice of laïcité, where friction with the Catholic Church over administration of churches led to entangling the French government in the process for nominating bishops, and where anxiety over overt expressions of Islam led to a ban on wearing conspicuous religious symbols in the public schools. If such laws were passed in the United States, liberal organizations like the ACLU would fight them as vigorously as they fought against mandatory school prayer.
In both liberal and conservative visions of the US Constitution, there is no recognition of religious communities as entities apart from voluntary associations of religious people. An American is free to profess the Catholic faith, pray according to Catholic traditions, and join with other Catholics to incorporate churches, schools, and so forth. Catholic voters and legislators may use their influence to move public policy in a direction closer to their religious beliefs, to the extent that the Constitution permits. But Catholicism as such is no concern of the state.
Our human relationships are defined by more than just citizenship; our religious affiliations are not just associations we have chosen, but reflect powerful feelings of identity. But American political activists who agree on little else share a disinterest in elevating those identities to legal personhood. The individual is both the object and subject of the law.
In other words: We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed.
1 Or, as one might say in Spanish, muy estadounidense.
2 As far as I can tell from Googling, Japan and South Korea do not have any kind of sectarian religious instruction in their public schools, nor do their governments sponsor religious schools.