Have you considered that properly vetted migrants are a completely different issue from potential terrorists?
The only way Islam can be rendered safe is for large numbers of Muslims to become enamored of our way of life (modern freedom of religion, etc.). Which requires them to experience the real freedoms the US offers.
Granted, unvetted migrants could include many potential terrorists. But if they are restricted to people who really are fleeing Islamic fundamentalism, they probably don’t involve enough risk to counteract the potential benefit of millions of Muslims who believe in modern-style religious freedom.
I’m not saying that’s where Tillerson is coming from, but AFAIK it could be. Do you have evidence it isn’t? Or are you just knee-jerking in terms of over-broad categories?