There certainly should be no registry by any government based on religion. However, refugees who are coming into the country should be registered and accounted for if there are national security concerns. A refugee's status is temporary in nature until one is able to return to their country of origin when feasible.
They're all registered and accounted for. And 'vetted.'
They're not, however, "temporary." When we let them in, they're in as permanent residents, and in 5 years they can apply for citizenship. They *can* go back to where they came from later on if they want to, but we don't let them in assuming they will -- we let them in assuming they'll stay here.
Freedom of religion isn't just for fundamentalist Christians or Mormons, but for everyone. This action is an example of protecting freedom of all religions.