Lutheran Synods are typicaly a bit easier. The German Free Church is Lutheran, and totally outside the state church.
The trouble is funding. The State collects taxes, and either gives it to the State church or to the Catholic church. People are not used to giving on Sunday.
Giving is always a problem in state churches because, as you say, people aren’t used to it. They regard the church as kind of a public utility.
The Europeans have a very strange system anyway,and even states that don’t have an official state church do some strange state funding of churches that actually serves to give the state some control over the churches or at least their schools.
In many European countries, education must be entirely state controlled, and the state “contribution” is considered to be payment for the schools and other social services run by the different churches (particularly the larger ones, such as the Catholic Church, Lutheran Church, etc.). The Catholic Church had long provided education, ranging from basic literacy taught by the village priest all the way up to universities, but at various times in the 19th century, the Church (and this probably applies to some larger Protestant churches, too) was forbidden to run schools and the state school system was established.
Of course, this gives the state enormous control over the curriculum and other conditions, which is not a good thing. But most parents don’t seem bothered by it, unfortunately.