If you want to go to church on Sundays, you are welcome to do so, but attending is optional. It's as simple as that. The established church of Denmark is Lutheran Protestant.
In the larger cities there are Roman Catholic churches. However there is only one Jewish Synagogue in Denmark, and that's in Copenhagen.
Most Danish churches are hundreds of years old. Try to visit a couple, as they are a part of the Danish culture and many are very beautiful, and make distinctive landmarks. It is inconceivable that you will be forced to attend church or be criticised if you do not. 99 per cent of Danes will respect your wishes, whatever they are.