It seems to be the case, but that is mainly because the government run churches stop to be living, and become political correct, dead institutions easily manipulated by anti-christian, liberal forces. But it is possible to have religious countries in both name and effect, and in fact it will be kicking christianity while it is lying down to separate the church and state now, and result in total unchristianity of the whole society in both name and practise.
But I still beliewe though that the church should be come economically and administratively (wich it is becoming more and more) from the state, but as it is the job of the government to protect Icelandic culture, it is the job to protect christianity as well, because it is an integral part of our culture. If we separate, what then? We will have to change everything in our society, even the flag.
The key point is that Christianity must influence the state, and not the other way around. If the state influence the church, pentacostals won't find themselves in a comfortable position, to put it mildly. But if the state is not to influence the church, the state also cannot pay the ministers of the church. The influence of the church on the state must be political, in the influence of the church on the (voting) public.It has to be pointed out that we in the US are accustomed to a system which contains too much government influence on the church, in the system of income taxation in which donations to churches reduce the official income on which we have to pay taxes provided that the government recognizes the particular church to which you donate as a "charitable" organization. A flat tax without deductions, or a national sales tax, would eliminate that problem, and will be resisted for that reason among others by the leftists.