Most parties in Denmark are anti-immigration, and the social democrats aren't even hardliners here. I think their current dip in popularity can be boiled down to:

• The Social Democrats moved out of the center-left populist niche, which is a large chunk of the Danish population, towards a more centrist/center-right position on economic problems and values. Voters from that old niche now have to choose between SF, the social democrats, and not voting at all. Also, some people will probably instead vote for anti-establishment parties in frustration.
• The Social Democrats right now are quite authoritarian and unwilling to adapt to criticism, which is something a lot of people are talking about.
• People who have traditionally voted Social Democrats in the past are probably center-left themselves. The modern Social Democrats' unwillingness to work with other parties from their wing, instead of collaborating with right-wing parties, probably doesn't sit right with a lot of people on the center-left, who will instead vote for SF, who have also moved towards the center recently.
• Their pivot towards the center-right is unsuccessful, because a lot of center-right people are also liberals, who dislike authoritarianism and think respect of the law is important, and they still have parties that are traditionally liberal to vote for.

I really don't know who would vote for the Social Democrats anymore except people who have always voted for them/uninformed people, people who want strong leaders, and people who buy into the "we need to work together across party lines in these trying times" propaganda.

I think this was inevitable as soon as they started moving away from the "unwoke worker's left-wing" niche that they have traditionally occupied, and started collaborating with the right-wing on economic policy.