The separation of church and state goes back long before Thomas Jefferson’s Letter to Danbury Baptists or to U.S. Supreme Court decisions banning school prayer in the United States. It goes back long before Canadians decided to large numbers to stop filling the pews of the local church and began viewing religion as something purely private matter. The truth of the matter is it was developed over centuries going back to medieval princes trying to secure control of local churches in Europe, hoping to make the seat of the bishop something they controlled along with the riches of the church.
And although arrangements have been made now and again, the Church has never ceded to the principal that she controls her own affairs, not the state.
When it comes to doctrine, canon law or personnel-- the Church does what she wants. And if the state doesn't like it, it can make martyrs out of us: we're not giving an inch.
That's why people left Europe. To run away from governments that thought they had the right to dictate to the people the doctrines and ethics of their churches.