How was the transition to civil marriage?

Today, it seems quite normal for us, but at some point someone had to inaugurate the civil marriage, make clear the insufficiency of religious ceremonies for legal matters. And in many cases, it was all very abrupt.

How did the transition from sole religious marriage to compulsory civil marriage work in Western countries? How did the believers, preachers and clergymen react around the world? When did people, especially the religious ones, finally get used to it?