Ireland was not an equal part of Britain. It was occupied by British soldiers, nearly all the good land was owned by England landlords, and the Irish could not vote for their leaders.
This unfairness and the often cruel way that the British dealt with the Irish lead to rebellion, which is were the Australian Catholic Church comes into the story.
There were a number of violent rebellions through out Ireland in the last years of the 1700s, including a large rebellion in 1798 - inspired by the American War of Independence.