What do you mean the migrant crisis stirred up things? The anti immigration position in danish politics has been a winning position since the mid 00's.
What is funny is that it has been pushed by the social democrats. See also what Labour have been doing in UK.
Whatever we call centre-left today we would have placed much further to right a couple decades ago. At this point even the US Democrats are more progressive than our EU "liberal" parties.
They saw Sweeden and freaked out, Denmark being already a nanny state.
As the crisis has worsened across Europe, Denmark started unbelievably intrusive AI-enabled mass surveillance of welfare recipients (almost 15% of the population), dangerous infrastructure which could be applied to the population as a whole. And I’d argue that fears over migrant-driven crime are what allowed Denmark’s politicians to push for Chat Control in the first place.