Couldn't they just not take in immigrants? This seems like a false dichotomy.
Nice? No. But what's the alternative, committing state-level suicide? That's why the first rule of rescue is ensuring the safety of the rescuer: if the rescuer is down, there's no hope left for the victim. And if Europe goes down, that will not help any migrants, either.
Any concerns regarding massive immigration, cultural differences, homeland security, etc. are labelled as xenophobic hate-mongering, despite plenty of evidence to the contrary.