Except in and near Reykjavik, the population of Iceland is thinly spread. Churches and congregations are tiny. A typical Lutheran church can't afford to hire a full-time pastor. That might explain part of the relatively low attendance.
For a truly secular country, consider the Czech Republic.
Religion in the Czech Republic was dominated by Christianity until at least the first half of the 20th century; since then it has steadily declined and today the Czech Republic has one of the least religious populations in the world. Religions other than Christianity make up a small minority, with the largest being Buddhism.
Historically, the Czech people have been characterised as "tolerant and even indifferent towards religion". According to the 2011 census, 34.2% of the population stated they had no religion, 10.3% was Roman Catholic, 0.8% was Protestant ... and 9.4% followed other forms of religion ... From 1991 to 2001 and further to 2011 the adherence to Roman Catholicism decreased from 39.0% to 26.8% and then to 10.3%; Protestantism similarly declined from 3.7% to 2.1% and then to 0.8%.
According to a Eurobarometer Poll in 2010, 16% of Czech citizens responded that "they believe there is a God" (the lowest rate among the countries of the European Union), whereas 44% answered that "they believe there is some sort of spirit or life force" and 37% said that "they do not believe there is any sort of spirit, God or life force".
Read more:
http://en.wikipedia.org/wiki/Religion_in_the_Czech_Republic
How indifferent are the Czechs to religion? When my wife and I were in Prague, we visited the grave of Tycho Brahe, which is inside the Tyn church. The church was practically surrounded by a maze of shitty little stores. We had a hell of a time finding our way to the front door of the church. There was a meandering path through the maze of shit, but there were no signs pointing to the path. I am not making this up.
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