As a citizen you have the right to believe what you want, that doesn't mean though that any kind of political party can be formed. Because the minute you allow parties whose politics are based on religion to be formed and to enter politics, it directly contradicts one of the main tenets your country was based on, and that is secularism. There are no absolute freedoms as you mentioned earlier, and you have to draw the line somewhere. For a secular democracy, I feel it's self evident that that line is there.
And, yes Denmark is a constitutional monarchy.
