Seeing how it brought a lot of criticism from the victorious powers I wonder what the political reasoning behind the asylum was. I'm aware there were ties between the Orange and Hohenzollern families but considering the extremely limited power of the Dutch monarchy at this point I am highly doubtful that this would have a significant impact on the decision.
Well, there's not one simple answer, but for one the Netherlands remained neutral all war long and the Dutch wanted it to stay that way. Neutral countries usually grant asylum to important foreigners. Especially when you're a monarchy, having ties with your neighboring monarchy, and the country next door kicks out its monarch. On the other hand, I think I remember that Wilhelm II wasn't allowed to move freely around the country, but don't quote me on that. But I'm pretty sure his "house" was in his family's possession for quite some time in 1918 and why should the Dutch have a problem with him living there? I know for sure the British tried to persecute Wilhelm, but I assume the Dutch didn't want to hand him over for some reason.