The meabning of a log cabin president simply means a president that came from a humble or common beginnings. Andrew Jackson is considered to be the first log cabin president. He was born in Crawford Plantation in a cabin.
Other notable examples of log cabin presidents are James K. Polk, Franklin Pierce, Abraham Lincoln etc.
The Church of England, Protestants, and puritans. The church of England was like get out if you don't join. Also they refused to support in parliament.