In Europe?
In Europe, conservatives (in terms of how the US see's conservatism) are all but gone and considered extremist fringe parties.
Basically nations in Europe usually have 3 parties. Liberals (who are called conservatives in Europe), Socialists and communists.
In the United States our liberals try to avoid being called socialists. They arn't very fond of the term. In Europe, their left leaning parties openly embrace the term socialist.
I must adres the occurring statement that the Church of Sweden is a so called state church. It is not, and haven´t been for many years. The church makes it's own decisions in any issues, and that includes the one in this thread topic. The church doesn't either receive any funding from taxes but is financed entirely on membership fees. The only money the church get from the government is some support for caring for ancient buildings like medieval churches and cathedrals.
This is correct. IIRC, the Church of Sweden broke with the State in 2000.
As far as know, this is the first Lutheran State church to break from the state, right?
Not quite. The Evangelical Lutheran Church of Finland and the state officially divorced "a few years" earlier. Namely, in July 1st, 1870 (and that's not a typo!). Although Finland does have a long and strong state church-oriented tradition, or national church, Finland does not have what constitutes a state church structure.
I predict within the next 20 years or so we'll see this in the US especially with Obummer types as President.