How has the impact of the Protestant Reformation influenced how we in America today view freedom, government, and rights?

The Protestant Reformation has had a profound impact in influencing American values, both in how they concern religious freedom and in the intersection between religion and government. The thing to keep in mind is that the Protestant Reformation created a lot of turmoil and tension throughout Europe, both through the prevalence of religious wars and also in the ways that governments and churches collaborated.
During the Early Modern Era, Europe was a continent in which different political states tended to have their own state churches. England had the Church of England and France the Gallican Church (Roman Catholic), just to name two. You can go further back toward the rise of Martin Luther and the political calculations of various princes as to whether they would patronize Lutheranism or stay under the aegis of Rome, or Calvin and his theocracy at Geneva, to see that this was a fundamental trend with deep roots in the past. Furthermore, be aware that state churches tended to suppress and restrict opposing ideologies. At the same time, be aware of ideology and anti-religious prejudice, which adds additional levels of complexity to this problem. Quite simply, Protestants and Catholics often held very negative views against one another, and these viewpoints have carried over, even in the United States. Despite official policies of toleration, prejudice and religious tensions have remained. For one example, consider the election of John F. Kennedy, the first Catholic president, and the concerns which circulated at the time as to whether he would be personally beholden to the Pope.
Regardless, the United States was created in a certain political context, and the influence of the Enlightenment (as well as the Enlightenment's reading of the religious situation in Europe) is quite clear. There is a very strong condemnation on superstition and intolerance that runs within the great writers and philosophers of the time period, and their influence can be found in the Bill of Rights—particularly in the First Amendment, which guarantees freedom of religion—and in the thought of men like Thomas Jefferson and his views on separation of church and state. These values remain critically important into the present day.