But there is racial prejudice in Denmark, most of it directed against local Muslim immigrants, who can be of Turkish, Palestinian, Iraqi, Pakistani, Afghani or African origin. In the 1960s and 1970s, "guest workers" were invited to Denmark to help fill a labour shortage, and in the 1980s and 1990s, Denmark made the noble decision to accept refugees and people who were persecuted or tortured. Many of these people came from rural areas, had little education, and were very conservative and religious. Of the more recent immigrants, many have had trouble finding work in Denmark and trouble fitting into Danish society.
There are certainly individual success stories - immigrants and immigrants' children who make important contributions to Danish life - but generally, there has been an unwillingness to integrate on both sides. Danish employers have not been quick to offer the immigrants jobs, which makes it hard for them to show what they have to offer. On the other hand, some immigrants see the Danes as unclean and immoral, and make great efforts to keep their children from becoming "too Danish." It's a story with no heroes.
What this means to you as a foreigner is that if Danish people think you are a local Muslim, they may be unkind to you - until they find out that you are not, upon which time they will be very courteous.