From Memory:

Latitudinarianism was a major faction of the CofE from before 1700, and when George Austen was at Oxford (in the 1750's and 60's) it was still going strong. There were always a few clergymen who didn't agree with Latitudinarinaism, but they were not really challenged until the 1730's. Samuel Whitefield and John Welsy started their Holy Club, or Methodists, at Oxford in 1735, and from that point on, the Methodists -under Wesley- and the Evangelicals- under Whitefield- provided some serious theological alternatives to Latitudinarian ways of thinking. Both factions originally tried to alter the Cof E from within, without a tremendous amount of success at first. The Methodists separated from the Cof E completley in about 1803 ( after Wesley's death, anyway) but the Evangelicals, for the most part, stayed within it, and waited out the course of the war. Between about 1805 and 1815, Evangelicalism became stronger than Latidudinarianism, and the latter finally bit the dust in the 1830's with the growth of what is known as the 'Oxford Movement'- yet another new wave out of Oxford University. But the Oxford movement are a different story, and beyond our timeframe, so if you don't mind, I'll stop right there.

George Austen was an Oxford man, and would have had much contact with both Methodists and Evangelicals whilst there- yet he did not join them, and as far as anyone seems to be brave enough to say, he stayed with Latitudinarianism until he died. Jane's own generation were not so unaffected- her cousin Edward Cooper became an Evangelical, and her brothers James and Henry flirted with them, too, but don't seem to have really gone over to the Evangelical side, at least whilst JA was alive.

Just for reference- I really don't want to stray too far from JA-it might be worth noting that Charlotte Brontë's father was born in Ireland, went to Cambridge, was curate in the much more industrialised North of England, and had very different ideas about educating his daughters than did George Austen. I think, but I'm not sure, that he was also an Evangelical preacher. He is also of a later generation than GA, and the much more "overt " Christianity of the Brontë sisters' writings must surely be as much of their later times as of their very different upbringing.

That's my take,anyway. I hope it helps....