My "Ancestral Rebellious Streak"

The Church of England is the official church of England. Protestant churches which do not conform to the Church of England doctrines are called nonconformist churches.

Register of Baptisms Kept at Providence Chapel, Spring Head, Saddleworth, County of York, [England], page 83, baptized 12 May 1835, Humphrey Eastwood; The National Archives of the UK, Kew, Surrey, England; database, "England & Wales, Non-Conformist and Non-Parochial Register, 1567-1970," Ancestry.com (http://www.ancestry.com : accessed 4 December 2017).

With his first wife, my third great grandfather had two children who were baptized in a nonconformist church. On Ancestry, these two baptisms are in a database titled "England & Wales, Non-Conformist and Non-Parochial Registers, 1567-1970." I found the first sentence of the description of the database to be thought-provoking:

Trace your ancestral rebellious streak through non-conformist and non-parochial birth, marriage, and death registers.

As someone from the States, I don't think I truly understand religion in England. What did it mean to be a nonconformist in England at this time? Did my ancestors really have a rebellious streak? And, since  James' children by his second wife, my third great grandmother, were baptized in the Church of England, did James' beliefs change? Did he just follow his wives' beliefs? Or did something happen in England that I need to learn more about?

I am enjoying learning about my "rebellious" English ancestors!