Anti-Catholicism has a long and storied history going back around 500 years to the beginning of the Protestant Reformation. Following Henry VII's split with Rome in 1534, anti-Catholic bias was elevated from being an articulated position within the Church to an institutionalized bias within the British government. This was codified with the Act of Supremacy, which replaced the Pope as the head of the Church with the English Crown.
The following centuries would be rife with Catholic/Protestant conflicts within England and, more importantly, between England and France. The Protestant Church, and English Protestants, would refer to the Catholic church as the Whore of Babylon, the Pope as the anti-Christ, and frequently use the word tyranny in association with Catholic rule.
This is very important to the founding of America, as this bias was imported with the colonists. This is evidenced through a number of early laws in multiple colonies that would forbid Catholic settlers, forbid Catholics from holding office, etc. This would eventually change with the passage of Religious Toleration laws, however suspicion towards Papists
would continue to bubble beneath the surface well into the 20th Century.
With Catholicism and the French inextricably mixed, the words tyranny, liberty, virtue, vice, etc. were commonly used in both political and theological arenas.
It is perhaps fortuitous for the birth of the United States that the Seven Years War occurred when it did. Religious leaders in the colonies had little difficulty getting their congregations to support the "liberty protecting" British against the "tyrannical" French. Preachers of the day used such strong language and imagery that tyranny became associated with anything and anyone that threatened the colonists way of life.
Within 2 years of the end of the war, the Stamp Act was passed. With the memories of the bloodshed still fresh in the colonists minds, it wasn't too much of a stretch for the religious leaders to subtly shift the target of who the tyrant was from the Catholic French and their Pope to the English Crown. I believe that this, along with Mayhew's Discourse, made revolution against their mother country a little more palatable to the colonists.
In essence, one could come to the conclusion that one of the major factors in the birth of the United States was the rabid anti-Catholic bias imported here by the colonists.