The Reformation actually started after Columbus's landing in North America.
Treaty of Tordesillas in 1494 was forced on Spain and Portugal by the Pope. The Pope basically said that all lands in the New World belonged to Spain and all new non-Christian lands in the Eastern Hemisphere belong to Portugal. No other Catholic countries can do anything in those areas without the approval of the owner.
The pope basically drew two lines on the globe setting the border. The western line started at the north pole cut half way through Greenland and ended at the south pole. The new world was everything to the west. Problem is that it ran through a chunk of Brazil which is why Brazil is an ex-Portuguese colony.
The Eastern line starts at the North Pole runs through siberia, through the pacific just west of Japan, and cuts Australia in half. Of course, Australia hadn't been discovered yet. Everything to the the east of this line is the new world.
Obviously, this treaty didn't hold up well, but the reformation gave the protestant countries an excuse to explore the new world since they didn't have to take orders from the Pope. Even so, France, a catholic country, ignored it too.
Really, the only country that was effected by the reformation in the exploration of the Americas was England. All the other countries, changed their religion once and then went to war with the nearest catholic country. Sweden became Lutheran and stayed that way. The Dutch Republic became Calvinists and stayed that way.
England kept switching. First it was Catholic. Then, Henry VIII made it protestant. Then, Henry's daughter Mary I made it catholic again. Henry's other daughter Elizabeth I (with the two hit movies) made it Protestant again.
Years latter, Oliver Cromwell over through the monarchy, executed the King Charles I, and established a Protestant fundamentalist religious military dictatorship. He outlawed drinking,smoking, gambling, theater, dirty books, sports, prostitution, and anything generally fun. He would have made Saudi Arabia proud. Basically, all you could do is work, pray, and die. Sex was allowed for creating children, but you couldn't enjoy it.
When Cromwell died, the people of England said enough was enough and brought back the King. Charles II kicked out the fundamentalists and brought back drinking, smoking, gambling, dirty books, sports, prostitution, and having fun during sex. Incidentally, those were also all his hobbies.
This brings us to the famous Pilgrims. They were part of Cromwell's crowd. They kept agitating a return to the no-fun policy. They annoyed everybody. They weren't persecuted for practicing their religion, they were persecuted because they kept trying to force their religion on everyone else. Sort of like Southern Baptists.
Charles II was the most easy going monarch in British history. Do realize how annoying you have to be to get him to throw you out.
Charles's brother James II was obsessed with turning Great Britain catholic again. After four years of trying, they kicked him and his followers out.
