It is entirely inaccurate. The depiction of the Puritan colonist instructing and evangelizing the compliant, submissive Natives is little more than a fantasy.

But more on the clothing. New England colonists often commented on how the Natives there wore less clothing, but they only wore less clothing when the climate merited it. You would not likely see a loincloth-clad Native in the freezing New England winter. And neither would you see many Puritan settlers wearing stifling dress in the summer either. And it would have rarely gotten so hot that the Native men would only wear a loincloth.

Puritan settlers also wore more than just gray and black and white. Their attire tended to be more colorful day to day. They would not likely have worn the buckles as they would have been seen as too ostentatious to daily wear. Any Puritan missionary would almost certainly be attired differently from the norm, more likely to wear the deerskin breeches and shirts of their Native audience than their Sunday best. That's mostly because the Natives were rarely willing to venture far away from home just to hear a preacher speak. It was more likely the preacher would head out into Indian country.

Puritan elites may have dressed in a similar manner on special occasions, but not often. The majority of non-elite Puritans would have dressed in a far more relaxed manner to better facilitate their labor. Pilgrim attire is not well suited to cooking, woodcutting, farming, fishing, sailing, or blacksmithing.

Sources:

• Sargent Bush, "America's Origin Myth: Remembering Plymouth Rock"

• Paul Heike, The Myths That Made America: An Introduction to American Studies