I will try to explain some conditions that led to Modern America being more religious than Australia.

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In America, televangelism became fairly common following WWII. This was bolstered when "in the 1970s and 1980s when the Federal Communications Commission (FCC) changed its policy of mandating free time for religious broadcasts to allow stations to accept money for religious programs. This regulatory change inspired more than a few preachers to use television as a means of funding their ministries.in the 1970s and 1980s, when the Federal Communications Commission (FCC) changed its policy of mandating free time for religious broadcasts to allow stations to accept money for religious programs. This regulatory change inspired more than a few preachers to use television as a means of funding their ministries." With widespread audiences, these televangelists were able to collect millions (Jerry Falwell had a net worth of ~$10 million when he died, and that is just his personal wealth).

These donations led to some of the Televangelists forming Christian and conservative political action groups such as Moral Majority and the Christian Coalition. These groups advocated that America was founded as a Christian country and they viewed that liberalism was weakening these Christian Ideals. they felt that "liberal thinking and policies had led the nation astray, and signs of decline were apparent: increasing drug use and sexual promiscuity, abortion on demand, the high rate of out-of-wedlock births and divorce, tolerance of homosexuality, absence of religion in the public schools, and court-supported attacks on public displays of faith. For fundamentalists, America's continued God-ordained prosperity depended on a return to traditional religious values and, by theological extension, a commitment to conservative political ideals."

These groups backed Ronald Reagan for president, and when he was elected, the fundamentalist, movement conservatives held serious power in government for the first time. "throughout Reagan's two terms in office, fundamentalists enjoyed a measure of public attention and success that would have been hard to imagine in the aftermath of the Scopes trial. Fundamentalists basked in the glow of their newfound strength and sought to retake the cultural ground that they felt they had lost to liberals in the shaping of law, education, the arts, the family, and politics. Liberals, by contrast, believed that fundamentalists had, in contravention of the separation of church and state, hijacked the political process and were attempting to impose their narrow religious agenda on the country, thereby undermining the United States' civil contract of democratic pluralism." In addition to contributing to the religious state of America today, the rise of Movement Conservatism also contributed to the deep split between the two main political parties of the United States.

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Sources

• Porterfield, Amanda. "Televangelism." Dictionary of American History

• Kenney, Jeffrey T. "Fundamentalism." New Dictionary of the History of Ideas

• Bruce, Steve. The Rise and Fall of the New Christian Right: Conservative Protestant Politics in America, 1978–1988

• Marsden, George M. Fundamentalism and American Culture: The Shaping of Twentieth Century Evangelicalism

You have to remember that the United States was founded after a number of groups fled Europe during the First Great Awakening that starts around 1730 and forms the early character of the nation that would come after. Many of the colonies were started by evangelicals from England and were joined by others from around Europe later on. Massachusetts as we all learned in grade school was founded by the Puritans. John Winthrop, an early governor of the colony, was a puritan minister that coined "shining city on the hill" which has been used since as a metaphor for the United States as a whole. The sermons of the puritans have had a profound effect on the creation of the American national myth and I would challenge the notion that evangelism as cultural phenomenon is a 20th century mass media creation.

Jonathan Edwards sermon, "Sinners in the Hands of An Angry God" is another evangelical text that has influenced the character of the United States. We see in it an attitude toward belief that is carried through all of the various evangelical traditions the United States has eventually produced. Within the man himself there is the embodiment of the duality in the American character of cultural accommodation and a tinge of zealotry.

One of the great American novels, Moby Dick, provides a similarly strident evangelistic thread throughout that draws on the tone of Edwards. Melville's Father Mapple who delivers a similar jeremiad that foreshadows the arrogance of the crew that are hunting the white whale. For both Edwards and Mapple there is an expectation that we as a people should live up to our highest notions of what good character is. These are all part of what makes up the notion of American exceptionalism.

These are the underpinnings of what have become a cycle of "Great Awakenings" in the United States that revive our notions of being a God fearing and exceptional people. They are divided into for distinct eras, First (c. 1730–1755), Second (c. 1790–1840), Third (c. 1855–1900), Fourth (c. 1960–1980). The forth is often disputed but I tend to think that it might not have ended in 80 or started in '60. We probably don't have enough distance to really sort out when or if it ended or for that matter begun. Father Coughlin starts his influencial radio ministry in the 20s, being considered one of the first to use the media to shape public opinion about politics.Where as now we have any number of religious figures telling us aspects of the administration and national body politic are either divinely supported or opposed with a mass movement of people that are often engaged to assert these perspectives. But I digress.

Many of the colonies and even some of our states were created as havens for specific religions, while Mass. was puritan in Pensylvania we have the Quakers and in Maryland the Catholics. Virginia was for the Anglicans and as time went on this led to friction with the Baptists. While contemporary readers are more familiar with the cultural domination of that denomination in the 18th century they were persecuted greatly. This would continue in many of the original 13 states and culminated in the "wall" metaphor regarding separation of church and state in a letter written by Thomas Jefferson to the Danbury Connecticut Baptists,

Believing with you that religion is a matter which lies solely between Man & his God, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, & not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should "make no law respecting an establishment of religion, or prohibiting the free exercise thereof," thus building a wall of separation between Church & State. Adhering to this expression of the supreme will of the nation in behalf of the rights of conscience, I shall see with sincere satisfaction the progress of those sentiments which tend to restore to man all his natural rights, convinced he has no natural right in opposition to his social duties.

Ironic that the man who would rewrite the Bible and leave out all of the supernatural stuff would both affirm the separation of church and state and invoking evangelical Christian tropes to ingratiate himself to his audience.

But Jefferson was a student of the classical world and understood the importance of faith even if he didn't share the evangelical zeal of some of his friends and neighbors. He would remark on his appreciation for the moderation of Adams' Unitarian Church all while acknowledging that for a Virginian in political life he needed to be an Episcopalian, although eventually he would express his disbelief in the "Trinity" which is one of the cornerstones of the Unitarian faith.

I often think many of the religious tests that come with contemporary political life in America draw on this acquiescence by Jefferson to the cultural notions around religion and trustworthiness. Although I think it was greatly influenced by his and his contemporaries that looked to the classical world for different ways to create our national story and institutions. In Latin the word "religio" means binding. The idea was some shared notions and mythologies were a way for a pluralistic society to show who they were and as a check to see who was loyal. As the Romans were fine if you were a mainly Christian household you were compelled to go through the motions of a shared ideology too. That's where the early Christians get into trouble in the empire, not because of their allegiance to Christ but because it precluded the participation in civic festivals and events.

You see that in Jefferson who flirts with all kinds of different perspectives on religion but keeps a more comfortable Christianity as part of his public persona. Currently we are led to believe that of the 535 United States legislators only one is an atheist. The atheist question comes up repeatedly in American politics and it gets swatted away by people we all know aren't religious at all.

This is mostly because we are brought up to conflate our national foundational myth with Christianity as the result of Evangelicals shaping our notion of who we are as a people. I'm not talking about Constitutional validation for the idiots who keep posting the ten commandment funereal monuments or state capitol grounds. This speaks to a deeper and often contradictory notion of our need to be both a secular and free society and hold a belief that we are a special and chosen people. Chosen not by virtue of ethnicity but by the virtues themselves. Indeed, I think that the affectation of religion that allows for a participation with and the strong statement of "God Bless America" and the "Under God" in the pledge need not be connected to any personal belief at all. We just need you to fold your hands and pray so that we can see your willing to set aside any personal belief and join the rest of us in how we understand ourselves as a people.

There is a line from the film Brothers McMullen where John Mahoney says "Sure I'm an atheist but I'm still a good Catholic." Essentially in the States it doesn't matter what you believe as long as you are willing to affect a civic faith that acknowledges some of the Christian mythos that is entangled in our national sense of identity. So while everyone in Australia was once a practicing Anglican; you all moved away from that faith along a similar arc. Your national identity almost requires a distancing from a national faith because of the more evolutionary movement away from the mother country. Where as our national identity had to sort itself out in a much different manner.

This is more of a social science question. There has been a study that correlates lack of social safety and welfare with religious observance but that simply redirects the question towards social safety in the United States.