Denmark is held to a higher standard because its a liberal democracy, and because it promotes a reputation abroad as a defender of human rights. Look at their foreign policy engagements and a significant amount is dedicated to democracy promotion, and it also promotes a self-image of a highly progressive,ethical society. Its a no brainer that a state like this will be held to a higher standard than a Saudi Arabia or China.
As for the situation in question, I am curious as to how many people actually have ever been to Denmark in this thread. Americans sympathetic to this style of demagoguery, always seem to buy into highly misleading right-wing tropes of no-go zones and out of control foreign areas. There is simply no such thing in Copenhagen (where majority of these immigrants live). The problem, to the extent of it, has to do with higher unemployment rates. The rest is highly exaggerated wolf tickets sold by politcians who recognize that immigration is a great wedge issue. Denmark's Muslim minority (and immigrant pop) at large is still only slightly above 10 percent of the population and its asylum claims have been dropping. Many Danes of foreign backgrounds leave the country for other places in Europe too, as EU citizens. Its hardly a population under siege.
As to why immigrants cluster in similar areas, study after study has shown that those type of clusters are generally a positive for economic mobility for new immigrants as it provides an informal support network, in ways the state cannot. In any case, Denmark heavily controls all aspect of refugee settlement, and in many cases settled people in similar neighbourhoods.
Reality is that its simply an xenophobic reaction to a (slightly) changing demography in a very homogenous country. I put the emphasis on slightly - ethnic Danes are still the vast majority population of the country and there is absolutley no truth to the idea that Muslims or any other immigrants are close to overtaking them. This is also another trope of the Euro right thats simply a lie - there is no evidence that any Muslim minority anywhere in Europe will come close to overtaking the majority population. In fact in all cases the birth rates of the Muslim population begin to mimick the majority population as quickly as the second generation. Just as the adopt simply socializaiton patterns, they also adopt the language of the country, its norms etc. There no second generation Danes who dont speak the language.
The Scandinavian countries are not the best places for quick integration of new refugees, at least early on because of very rigid labour markets, harder languages to learn etc, but it does get better in future generations. But still not as good as Canada or the United States or even the UK, which is an interesting contrast/question.