Final answer:
It is likely that Gayden, the Pennsylvania blacksmith, was a Quaker since William Penn, the founder of Pennsylvania, was a Quaker and the state's early settlers were often seeking religious freedom characteristic of Quaker beliefs.
Step-by-step explanation:
To infer the religion to which Gayden the Pennsylvania blacksmith belongs, we must consider the historical context of Pennsylvania's early colonists. Like many of the early settlers in the New England colonies, those who settled in Pennsylvania were often motivated by religious freedom. William Penn, Pennsylvania's founder, was a Quaker, which suggests that Quakerism had a strong presence in the early culture of the state. Quakers, part of the Society of Friends founded by George Fox, believed in the idea of an "inner light" and social equality, rejecting societal hierarchies and addressing all individuals as equals.
Bearing in mind the values and beliefs of the Quakers, and the influence of William Penn and Quaker religion in early Pennsylvania, it is likely that Gayden, as a blacksmith living in this historical period and region, could be a Quaker as well. This inference can be made even stronger if Gayden exhibits the egalitarian and direct manner of speech, or other cultural and social practices characteristics of Quakerism. However, without more specific details about Gayden's personal religious practices or statements, one cannot state with absolute certainty to which religion he belonged.