The church in Austria is by no means a pushover, and even though it has now declined, the church still colludes with the local nobility. The upper echelons of the church are essentially made up of relatives of the nobility.
That's why Franz wasn't rushing to take action against the church; it's a situation where pulling on one thing affects the whole. You have to eat your meal one bite at a time, eliminate your enemies one by one, and if you can turn an enemy into a friend, that's all the better.
Without a doubt, Austria's church members are not worth wooing. They are rich and obstruct the development of Austrian society, making them genuine reactionaries through and through.
Prime Minister Felix began, "Your Highness, it would be best to postpone matters concerning the church. Recently, a change of events occurred in the Papal State, and Pope Pius IX has sought refuge in Naples and called for our help.