The refusal to reproduce is not at the core of all this. The Danes would be fine with fewer Muslims. The Muslims are the problem, not the Danes. If the two groups tryed to out-breed each other, would that solve anything?
It is the fact that Westerners have largely stopped reproducing that 1) caused governments to increase immigration in order to have more workers paying into social security systems, and 2) have allowed the proportions of said immigrants to grow rapidly.