@Olivier5,
Certainly the position of religion in any society is conditioned by that society's experience of religion and its effects. When i read Pagnol's
La Gloire de mon père, i was impressed by his assertion that many teachers in public schools in the late 19th and early 20th century felt they had a duty to combat the influence of the church. I can't speak to the accuracy of the image he presents, but it gave me a lot of food for thought.
The history of religion in the United States is conditioned not just by American history, but by the history of England before the revolution. Just at the time that settlements on the North American continent were growing, England began to slide into the religious quagmire which lead to the civil wars of the 17th century. After the restortion of the Stuart monarchy in 1660, Parliament moved to exclude anyone who was not a member of the Church of England from public office (c.f. the various Test Acts and the Occasional Conformity Act).
People left England for the "new world" during the civil wars, and some people already in North America returned to fight ni the civil wars--although in far fewer numbers than those who fled England. This experience of religious turmoil and the attempted imposition of religious conformity strongly influenced political thinkers in what became the United States. The first amendment to the constitution to be ratified begins: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof . . . " (that amendment also protects freedom of speech, of the press and the right of assembly).
The states of Massachusetts and Connecticut had religious establishments--you had to pay a church tax to the Congregational Church, whether or not you were a member. Those who weren't members were also often excluded from public office. Even most contemporary Americans won't understand this because of "incorporation." The rights guaranteed to people under the national, federal government have been extended to cover all the states. That was not initially true. So it was taken that the Federal government could not establish religion, but that the states were not bound by that stricture. The congregation of the Danbury, Connecticut Baptist Church wrote to Thomas Jefferson in 1802 to complain of their position as a result of the state's religious establishment. Jefferson's reply has become famous because of his use of the expression "wall of separation between church and state." Of course, this was the typical flannel-mouthed politician--Jefferson had no authority to intervene on behalf of the Danbury Baptists.
Since that time, as the Federal courts and the Supreme Court have "incorporated" constitutional civil rights, applying them to the states as well as the Federal government, the first amendment prohibition on religious establishment has been very much in evidence. It has been successfully used to prohibit prayer in public schools. It has been used to prohibit the teaching of religious creationism in public school science classes. Probably the most important case was Lemon versus Kurtzman, which resulted in the "Lemon test" to determine whether not state legislation constituted an establishment of religion. (In the Lemon case, and an earlier case in the First Circuit, laws in Pennsylvania and Rhode Island respectively which reimbursed private schools [chiefly Catholic schools] for teacher salaries and educational materials were struck down.)
Since the era of the younger George Bush, though, things have changed. Politicians first feared and courted religious conservatives, and subsequently learned that those religious conservatives did not wield anything like the electoral power it had once been thought they commanded. The tide of religious conservative political power rose and fell all within a few years time. This has been complicated by the decision of the Supremes in Greece, New York case. The city council of Greece, New York had begun having a prayer service to open their meetings, and this was challenged in court. The Supremes decided that it was acceptable as long as no one religious confession was favored over another. This has turned the trend of American reaction to religion in public life on it's ear. That decision ignores that the majority of religious confessions in the United States are christian, and that if one gave each minister of a congregation his or her shot at conducting a prayer service, the long-term tenor and effect would be decidedly in favor of christianity. The Supreme Court is the most arbitrary and authoritarian institution in American political life--there is no appeal from their decisions except to amend the constitution. The Greece, New York case is troubling because it appears that the Supremes have ignored or even overturned an existing amendment. Supreme Court justices are appointed for life, so this extremely conservative court will likely last a long time.
The early republican history of the country was decidedly anti-establishment while not necessarily being anti-religious. Andrew Jackson, for example, refused to call a national day of thanksgiving and prayer after a cholera epidemic in the 1830s. This began to change, however, with the first Republican president, Abraham Lincoln. He was not known as a particularly religious man before he was elected president, but he often had god in his mouth afterward. He established the national Thanksgiving holiday, although the religious character of that holiday has faded before the appeal of wretched excess--it is mostly seen now as a day of approved gluttony and televised football. It was also during his administration that "In God We Trust" was added to the coinage.
This is getting tediously long, so i'll just observe that there have been times when frenzies of religious devotion (probably phony on the part of politicians) have waxed, and times when they have waned. The essential religious character of the nation, however, remains largely unchanged. The public issues have been taken to Federal courts, an by and large, the courts have excluded religion from public life.