No one (except terrorists) believe we should allow immigration of likely terrorists into our country. The question arises in the interpretation of likely.
Our mass media (NY Times, Fox, Washington Post, Huffington Post, etc) should present a running total showing terrorist violence to date. It shows that terrorism results primarily from the Islamic Civil War.
The Sunnis (ISIS, Al-Qaeda, Humas, Muslim Brotherhood) and the Shias (Iran, Hezballuh) are killing each other in suicide bombings and mass murders.
The week I assembled this chart in mid-2016, there was a violent terrorism attack in the West.
Adding columns for home-grown and foreign-born terrorist in the West would be a useful fact to guide sensible policy making.
The likelihood of an attack in the West could then be assessed as we assess other life-threatening events, such as gun violence, car accidents, and the grave illnesses.