I think you may be confusing the Pilgrims and the Puritans. They were two very distinct groups. The Pilgrims came over on the Mayflower. The Puritans are the ones associated with stringency and Hawthorne's Scarlet Letter.
It's probably only funny if you've had some exposure to evangelical culture. John's description of it as "the Onion for evangelicals" is perfect. It's evangelicals poking fun at evangelicals--who are only one of many Christian subcultures, by the way.