> You can restrict immigration in a humane and respectful way
But this won't change anything, if their demand is not reasonable, or founded in truth to begin with. As I said, the AfD is most popular where there are no migrants at all. Lots of them feel their narrative validated when they see a brown person existing, see "Turkish" people living here for generations. The goalpost will always shift. You will never satisfy them, if their demands aren't anchored in reality. Again, this isn't fueled by exposure, but guided media outrage. There is a lot of conspiracy narratives mixed in as well. Talk to them, poke deeper than the concern trolling surface. You will encounter actual loony talk quite soon.
Apart from that, the biggest problems with these ideas are factors outside of Germany's control. E.g. if the origin country won't accept those immigrants back, you can't just air drop them there. Constitution, European law, human rights, Schengen... it's not really possible/worth it to do anything significant. It's all ever going to be for show.
On the contrary, demands that aren't founded in reality are often easier to satisfy, because pure rhetoric can shift the narrative much more easily than it can shift reality. Going back to Denmark again, if you pulled out charts and tried to track the objective quantity of immigration, you'd have a hard time identifying any policy shift. But as you say, immigration restrictionists were never looking at these charts in the first place. What matters politically is that the center-left PM goes around talking about how mass migration can be dangerous and the preservation of Danish culture is valuable.
Honestly, I get the impression your objective is to get a foot in the door for a certain idea, so to speak. Concern trolling ("just" preservation of Danish culture, huh?!), constructing a narrative where legitimizing neonazi parties through compromise is without alternative. You are not even addressing the foreign influence with these movements, the threat of social media reality distortion. Although, you tried to preemptively diffuse political association, I don't believe you are arguing in good faith. My answers are meant for everyone else reading, since I think it's wasted on you.
The CDU ran their election campaign on "anti-immigration" and continues to perform this rhetoric. So far the AfD poll numbers have been climbing, so ... your premise is evidently just wrong. This has been debated to death and I think for the general case, political science agrees that people will choose the original, when moderate parties pander to populist ones.
I am not familiar with the Danish situation. It's a very small country, with little land borders. Germany is large, bordering nine countries. It has a very high population density, large global economic influence, and a very unique history in regard to unification as German Reich, industrialization, revolution, fascist and communist dictatorships, war and division, and contemporary reunification. There is a very, very distinct geographical correlation with AfD voters and the former DDR territory.
Most people here are very fine with Germany's lack of nationalism and flag identity. We never really had a unified cultural or religious identity, since what's considered "Germany" has been quite radically changing in the last 300 years. (I think Rammstein's "Deutschland" does quite a good job expressing this feeling: https://www.youtube.com/watch?v=NeQM1c-XCDc)
You are also suspiciously discounting the impact these populist narratives and policies have on the lives of those matching the appearance of the scapegoat targets. Overall the neonazis' demands are not "just" a "sane" immigration policy, but open calls in particular for deportation, even deportation of German citizens. And they are also calling for de facto suppression of women's rights and LGBT lives all together. Oh, and what about the newly found Russia fandom and climate change denial? What's your take here?
Should we give in there as well? And if not, what's the difference?
If you want to win AfD voters, what you fundamentally have to do is present a vision that inspires AfD voters and convinces them to join your side.
Does this mean adopting AfD positions and trying to water them down a bit? Not necessarily, I agree that populist-lite is always going to lose to the original. But it means convincing immigration skeptics, gender traditionalists, perhaps even Russia fans and climate change deniers that they're allowed to be on your side. It's a hard but necessary line to straddle. I struggle with it myself - I spent a while over the weekend trying to find some good flyers to leave on people's Teslas, until I sat down and asked myself why none of the major protest organizers are encouraging this.
And once you start thinking within the realm of strategic moderation, immigration sticks out as an obvious compromise to make. Restricting immigration has few catastrophic downside risks, is easy to roll back if circumstances change (unless you do it in a catastrophic Trumpian way...), and unless your population pyramid is really unhealthy doesn't involve many tradeoffs with other policy areas.