Religious toleration does vary from country to country and over time. Saudi Arabia today, for example, would represent an extreme of religious intolerance, quickly jailing people who practice non-Muslim faiths outside of carefully-prescribed international zones where foreign nationals tend to cluster. Likewise, Nazi Germany maintained a high level of religious intolerance, not only exterminating Jews, but persecuting people who deviated from strict Aryan Protestantism or Catholicism, such as Quakers and Jehovah's Witnesses.
As for the United States, religious tolerance has been a mixed bag across our history, and religious freedom has not been allowed as broadly as we might expect. The Puritans, for example, set up a theocratic state that did not allow deviation from official Church doctrine as they understood it: they did not come to the New World in pursuit of a generalized religious freedom but for the freedom to worship in their particular way. However, when Quaker William Penn established Pennsylvania, he intentionally opened the territory up to non-Quakers, such as Mennonites and Amish, who were persecuted in their home countries. He was also tolerant of Native American faiths. From the start, therefore, America has experimented with a diversity of approaches to faith.
As the American colonies became the United States, the concept of religious freedom was enshrined in the Constitution, but for the first century and a half of U.S. existence, not interpreted nearly as liberally as today. For example, Native American tribes on reservations had to convince authorities that some of their rituals, such as dances, were actually religious practices, and often had to bring "heathen" practices into a specifically designated religious building, akin to a church, to have these practices accepted as faith expressions (though it was a violation of the original cultures to separate religious worship from the rest of life). Mormons also had to struggle to have their faith accepted as legitimate.
On a political level, the Ku Klux Klan grew in the 1920s largely because of Protestant fears of Catholicism. Jews also had to work hard in the early twentieth century to convince authorities that their faith practices showed that they were a religious group, not a "race." Black churches, especially those that preached separatism, could find themselves under FBI surveillance and persecuted. Many books have been written on the topic of the U.S.'s spotty record on religious freedom. One that is an accessible starting point is Steven Waldman's Sacred Liberty: America's Long, Bloody and Ongoing Struggle for Religious Freedom.
I would say the U.S. experience has been different from that of most cultures since the fall of the Roman Empire, as we have been more of a melting pot, and more of a pluralistic society than many others. So although our record of religious tolerance has been highly imperfect, it has been an ideal to which we aspire, and we have done better than many other cultures historically.