Well they aren't really taken in as refugees. Western leaders won't admit that they have created societies where people don't have enough children and they are really taken in to fill in population gaps. And Muslim countries are one of the few countries still having children.

In other words western societies are no longer self sustaining. They don't necessarily need all this labor but they do need to keep up their populations in the long run to stand a chance against future wars, against other countries (i.e. Muslim countries) which will significantly outnumber them.

But still not a good strategy if the plan for future wars is to be Muslim countries vs Western armies with significant Muslim populations.