One main event that led to the political and religious changes in British North American from 1720-1770 would have been immigration after 1730. Approximately 500,000 Europeans, primarily from Germany, Scotland, and Ireland, immigrated during this time. As this immigration continued, much of the population would not have been original colonists (or their descendants, rather), so a shift in culture and religious beliefs would have occurred. Specifically, many of those immigrants would have been Catholic leading to a conflict in religion.
A second event would be the development of schools. As more schools developed, more people became intelligent. These schools began as religious institutions, but quickly shifted to become more secularized. In other words, the schools would have become more concerned with what was happening globally (politically, etc) and not have so much concern for religious meanings.
A third event, due to the crisis of many cultures in one place, would be the rise of religious concern. Each immigrant strove to find their "group" of similar religions. In other words, when a group of people enter another country, they face a choice--do I abandon my culture and become "normal" or resist the "normalcy" and maintain my cultural beliefs. At this time period, many people were clinging to their cultural beliefs because they lived with similar people (Irish with Irish, etc.).
Finally, the French and Indian War and King George's War, since they occurred partially in the New World, caused taxation on the colonists primarily in New England, which in turn caused the colonists to feel anger toward the England. Many colonists bcame disenchanted with being associated with the British crown. There was no representation for the colonies in England (and they didn't ever see the King because of the distance). Ultimately, the colonists felt great disdain and disconnect from the European governments (primarily British).
One more thing, the First Great Awakening was a religious awakening. More and more traveling pastors and revivalists would reach out to all sorts of people--minorities--and evoke strong emotions in crowds. This caused many people to feel strong reactions (mainly positive) toward religion and towards God. This would have occurred mainly in the 1760s.
There are two main events that contributed to the changes that you are asking about in this question. One of these events mostly impacted religion while the other mostly impacted politics.
The event that brought about mainly religious changes in the colonies was the Great Awakening. This event is generally said to have started during the time period from 1739 to 1742. This was a major change in which many colonists came to have a more personal and emotional connection to their religion. It also led to splits in many churches between “old lights” who adhered to traditional views of religion and “new lights” who had been affected most strongly by the Great Awakening. This religious change also helped influence politics since the new religion was more egalitarian and emphasized the idea that people could make their own choices rather than simply obeying those above them.
The event that affected politics was the French and Indian War. This war cost the United Kingdom a great deal of money. Because of this, the government of the UK wanted to assert greater control over the American colonies. By doing so, it would be able to control colonial trade and would be able to get more money in taxes from the colonists. As the British government enforced its laws more strongly and imposed more taxes, Americans became more and more inclined to rebel. This led to the Revolutionary War.