Like many things that humans do, the stated idea or ideal has little to do with what is going on in the subconscious as well as in actual practice. Only about 2% of what we consider to be thought is conscious - the rest is coming out of stereotypes, cultural narratives, religious and parental teaching, etc., and other manifestations of the collective unconscious.
The Pilgrims and Puritans certainly were intolerant by design, but as time went on, this becomes less overtly intentional, but not necessarily all that much better.
I linked you this elsewhere, but it's such a great example of what I'm talking about that I'm adding it here as well.
"In newly independent America, there was a crazy quilt of state laws regarding religion. In Massachusetts, only Christians were allowed to hold public office, and Catholics were allowed to do so only after renouncing papal authority. In 1777, New York State’s constitution banned Catholics from public office (and would do so until 1806). In Maryland, Catholics had full civil rights, but Jews did not. Delaware required an oath affirming belief in the Trinity. Several states, including Massachusetts and South Carolina, had official, state-supported churches.
Even as late as 1960, Catholic presidential candidate John F. Kennedy felt compelled to make a major speech declaring that his loyalty was to America, not the pope. (And as recently as the 2008 Republican primary campaign, Mormon candidate Mitt Romney felt compelled to address the suspicions still directed toward the Church of Jesus Christ of Latter-day Saints.) Of course, America’s anti-Semitism was practiced institutionally as well as socially for decades. With the great threat of “godless” Communism looming in the 1950s, the country’s fear of atheism also reached new heights."
Even today we have rampant anti-semitism, rampant anti-Islamic sentiment, and continuous insistence that this is a "Christian nation." Boarding schools for Native children didn't end until 1969. In these schools they were forced to give up their own spiritual traditions in favor of Christianity.
Despite the rhetoric, there is very little history in practice of actual religious tolerance in America.