The two most important kinds of pluralism that were found in the United States during this time were religious and ethnic pluralism.
Ethnically speaking, this was the time of the first major wave of immigration to the US. This wave saw Germans fleeing political repression and Irish fleeing the potato famine. Both groups were new to the country during this time and were not particularly well-assimilated.
In terms of religion, the US was more diverse than ever during this time. The Second Great Awakening and the market revolution had led to a great deal of religious change. This was the time of the Millerites/Seventh-Day Adventists and the Mormons and of splits between northern and southern wings of denominations like the Methodists and Baptists.