The narrative suggests that the information in the charts represents church members or adherents. But I interpret the chart is really demonstrating that some religions expanded and not that others declined.
There's another chart here
https://books.google.com/books?id=9ACdjfz6hcEC&pg=PA16 in the same book, which gives "rates of religious adherence" and shows the percent doubled from 17% to 34% in the period, not even counting the actual population increase. So it seems like you said that there was an expansion, probably due to the revival/camp-meeting era, where Methodists started the sing, shout, jump recruiting of rural working class converts, and some of the Baptists and Presbyterians followed, but Episcopalians just couldn't bring themselves to stoop to such embarrassing displays.
I don't quibble with the book's assertion that religious diversity increased after 1776. Swedenborgian is listed in the 1850 census as a religion with in 1850 with 5475 accommodations. Religion was so important that obscure theologies attracted significant numbers of adherents.
There was also that strange period 1820-1840s, where new religions sprung up like mushrooms after rain, mostly in New England: Transcendentalists, Mormons, Millerites, the various utopian societies like Brook Farm, Oneida Society, Spiritualists, Shakers got a foothold...
I suspect not, politics was still dominated by Presbyterian, Episcopalian and Congregationalist white men.
Yes, a lot of the camp meeting converts were from the lower classes.
The Census information in link doesn't actually provide counts of members, rather "accommodations" , which is "capacity to accommodate worshipers at one time"
The online Historic Census Browser has the information available, and I've always found it frustrating that you can't get what everybody wants to know: How many Baptists were there? (Or whichever religion.) Ministers, buildings, accommodations are okay for comparative work, but even then there's the problem that a lot of poor, fast growing denominations had circuit riders who might preach once or twice a month while laymen filled in the other Sundays, and they might meet in someone's house. So it's not apples-to-apples with an Episcopal church with its own dedicated preacher.
My whole purpose in this is to get a handle on how various Christian sects compared in numbers in around 1830-1860, so I can say it's a big deal, or not, when the Methodists, Presbyterians or Baptists split over slavery.