Obama chose the term “religious test” because it comes from the Constitution, which prohibits a religious test for public office. But the Constitution does not prohibit a religious test for refugees–and, indeed, without it our policy would be less compassionate.
In the present crisis, we can and should prioritize Christian and Yazidi refugees, as well as Iraqis of all faiths who helped the U.S. during the war, whom the Obama administration shamefully abandoned. We could also admit Muslim refugees who can show that they qualify for that status due to religious persecution, and perhaps for other compelling reasons.
But simply to commit to taking in tens of thousands of people–more, once their families become eligible to immigrate–is a dubious policy, especially when the international community has done next to nothing to stop the war that remains the root cause of the ongoing Syrian exodus. The fact that terrorist organizations have clearly learned to take advantage of the refugee exodus is another reason to reconsider.