The Age of Exploration, also known as the Age of Discovery, describes the expansion of European influence on a global scale.
The explorations went west after the Ottomans blocked Constantinople. The Europeans needed another route. So they took the path available — the Atlantic Ocean.
The period was funded from, not the Reformation or Rome, but the wealth of the Renaissance. The spice trade provided a large part of the financing. This need for preservative spices was a matter of survival. Not long before this time The Plague had killed about 2/3 of the population of Europe. The new goal was to both survive and advance. That is, after all, what all people do.
The age of exploration provided an avenue for missions, both Protestant and Roman. Remember: Rome had a difficult enough time financing one venture, the Sistine Chapel. It’s not like they had a lot of money available at the time. And the Protestants — they were still trying to build allegiances and secure locations.
Exploration was a secular venture.
Yes, too often the Christian conversion message was a call to allegiance rather than faith. Christians and the nations of Europe had just stopped the coercive conversion efforts of Islam in Europe. Spain had just been freed shortly before Columbus sailed. This, in fact, is what allowed the financing of his venture. For a period of time Christianity adopted the same method as employed by Islam.
The Pilgrims were not part of the age of exploration. They were not merchants. Nor were they financiers. They were escaping persecution. There were those who came after them who committed atrocities. But it is not the Pilgrims who are to blame.
The narrative is that Europeans brought violence to an otherwise peaceful people in the Americas. Such is the naive treatment history receives. The impression is not made by explicit remark by by exclusion. That is, if Europeans brought violence then violence was something external to these people. It is all the fault of the Christian Europeans as the revisionists would say.  
You can now see the disconnect. Was it Christianity or was it the secular economic venture which initiated these wrongs? (I will not excuse the wrongs of Christians here. But neither is it appropriate to not make this distinction as Christianity makes no proposition regarding economic plundering. That remains in the purview of the secularist.)
Today Christians still evangelize using the mechanisms of secular exploration and economy. We will fly on their planes, ride their ships and trains, and drive their cars.
Christianity was not the origin of Manifest Destiny. Manifest Destiny is a strange mix of ideas. It is very secular and nationalistic. It employs the optimism of and borrows the eschatology of postmillenial theology. It also specifically represented the racism of the Democratic party. 
Yes, too many Christians went along for the ride. That is to our shame. But to blame us for what was done by the atheist, secularist, and nationalist — that’s historical revisionism.
 To be precise, Islamic law enjoins forced conversion. The consequence, however, is either submission to the point of desperation or even death for Christian, Jew, and infidel (the godless). It hardly seems consistent.
 Keeley, Lawrence, War Before Civilization: The Myth of the Peaceful Savage (Oxford University Press, 1996)
 LeBlanc, Steven, Constant Battles: The Myth of the Peaceful, Noble Savage (Saint Martin’s Press, 2003)
 http://www.history.com/topics/manifest-destiny, cited 11/27/2014
“Originally a partisan Democratic issue, ‘manifest destiny’ gained Republican adherents as time passed.”