The problem is that the Evangelical Lutheran Church is the established (state) church in Denmark.
http://en.wikipedia.org/wiki/Church_of_Denmark
The UK parliament could probably do the same to the Church of England. Non established churches in Denmark are not affected
Interesting quotes from the article:
“Fewer than 5%[citation needed] of church members attend services every week. However, the church is still widely used for traditional family ceremonies including christenings and confirmations. In the year 2008, 41% of weddings and 89% funerals were performed in the National Church,and 71% of adolescents in grade 7-8 were confirmed.
“According to a 2009 poll, 25 percent of Danes believe Jesus is the son of God, and 18 percent believe he is the saviour of the world.”