Also, it may be of interest to US readers, - being a federal set up too - I often hear Americans listing their loyalties, (Pence, I think, publicly proclaimed he was Christian, American, Conservative, in that order.) 

The Swiss are Swiss first. They all absolutely value their democracy, often holding referenda on important issues. They don't have to wait on a new government to change things. Any outside body which attempts to interfere with that will get sunk.

This happened when Benny attempted to impose an ultra conservative Bishop in the diocese of Chur against the will of the Catholic people. On the day of the Episcopal ordination, thousands of Catholics turned up at the Cathedral and blocked the entrance. The Bishop 'elect' was driven away and the ordination cancelled. Benny then had to create a new diocese in Litchenstein to dump the poor guy. 

The US Catholic Church should be doing the same. Sensus Fidelium rocks in Switzerland.