One of the main purposes that promoters of the Virginia Company gave for the continued development of the Jamestown Colony was the Christian duty of converting the Virginian natives to English religion and English culture.  In the view of many English people, the Native Americans were "savages" who would receive the gift of civilization from the English colonists.

In George Chapman's The Memorable Masque of the Two Honourable Houses or Inns of Court, which Chapman wrote for the wedding celebration of King James' daughter in 1613, the "Virginian Priests" who arrive to present King James with gold from their country, convert to Christianity after seeing the English monarch, who outshines the sun, their previous object of worship:

In John Fletcher's 1622 The Island Princess, the title character Quisara spontaneously converts to Christianity when she observes that Portuguese adventurer Armusia would rather die than suffer a forced conversion to Islam at the hands of the colonized natives of the Molucca or Spice Islands:
     

Explicit religious conversion was not the only means by which the English, and other European colonists, sought to "civilize" the native populations they encountered.  The plays of the period show us other sorts of cultural conversions.  Many English colonists thought that teaching native Virginians was the first step in converting them to Christianity.  In fact, one grammar text of the period contains a forward suggesting the book's use for converting the "savages" in Virginia.  Shakespeare includes a complex discussion of language conversion in this scene from The Tempest:

Although Shakespeare's Caliban is not literally a Native American figure, many scholars have identified him with Native Americans, in part because Shakespeare's sources for the play concern the colonization of the New World.  Certainly the relationship of Prospero and Caliban has some parallels to the relationship between colonists and colonized peoples, and this passage about Caliban's acquisition of Prospero's language demonstrates the negative results of a forced cultural conversion.

Another example of the association of the English language with potential religious conversion comes from Phillip Massinger's 1632 The City Madam.  Massinger creates a nonsense language for his fake Virginians, Englishmen who have disguised themselves as Native Americans, and another character despairs of being able to convert them to Christianity if they can't speak English:

The image of Native Americans as cannibals was widespread in both non-fiction publications and the drama of this period.  Ben Jonson, in his 1626 play The Staple of News, describes plans for a gastronomic conversion:

By this time the English fervor to convert the Virginian natives was so entrenched in English cultural discourse that Jonson was able to satirize the practice of cultural conversion.

The Staple of News also contains a reference to what members of the Virginia Company considered their greatest conversion success.  The Powhatan princess Pocahontas, Matoaka as her own tribe members called her, was the first native Virginian to convert to Christianity.  She subsequently married English colonist John Rolfe and traveled to London with him and other members of her tribe in 1617.  Her voyage was in part a sort of publicity junket for the Virginia Company, and she even attended masques at King James' court and there met Ben Jonson.  Jonson refers to her visit to London in this scene from the play:
    

Along with the desire to convert "savage" peoples to European religion and culture came the fear that Europeans had of being converted themselves.  Many of the plays from this period feature the threat of forced religious conversion.  Day, Rowley, and Williams' The Travels of the Three English Brothers, about the lives of the real-life Sherley brothers, glorifies Sir Thomas Sherley's resistance to the Great Turk's demands that he convert to Islam:

Forced conversion to Islam comes up again in Fletcher's The Island Princess, as the colonized natives of the Molucca Islands attempt to convert Portuguese colonist Armusia.  In this scene, the beautiful native princess Quisara requests that he convert out of love for her:

Here Fletcher conflates Islam with worship of the sun and moon, thereby creating a generic "other" religion, which threatens the Christian European colonist.

Another European fear surrounding exploration and colonization seems to be the fear of "going native."  In Fletcher's The Sea Voyage, the trauma of being shipwrecked on an island off of South America leads the would-be colonists to consider cannibalism:

Europeans often described Native Americans as cannibals during this period.  Interestingly, stories of English colonists having committed cannibalism also circulated after the "starving time" of the Jamestown Colony."

The Sea Voyage also presents a group of Portuguese women, former colonists, who have become Amazons after living on an island for years.  These women enact a ritual of human sacrifice reminiscent of descriptions of Aztec rituals by Spanish colonists of South America.

The desire to create new Europeans by converting colonized people, and the anxiety over the possibility that European colonists might be the ones to ultimately change their identities, suggest that the exploration and colonization occurring during the Early Modern period raised questions about the stability of cultural and individual identity.  If English culture could travel in one direction, it might also be possible that the new cultures that the English colonists encountered could profoundly affect English society and culture.