The Bishops, too, rely on the state to enforce their right to practice their religion freely within the state.

This is of course true, although only to an extent, and it is certainly part of the Catholic Bishops' narrative in the US, for example, regarding the new requirement of employers to provide free birth control to employees. But the Catholic Church has only come around to accept the concept of "freedom of religion" since Vatican II, and it was controversial even then.  The mental framework that puts the Church above the state and that makes the state's institutions subservient to the teachings of the Catholic Church, even in states where Catholicism is not the majority religion, remains quite strong among many, even in states, such as Mexico, which formally renounced any institutional connections and went to the trouble of rounding up and killing priests to make the point.

I predict it will be a long time before Ireland gets comfortable with the concept of a true separation of church and state -- in practice as well as just nominally -- based on other Catholic countries' experience.