Contrary to popular belief, Trump does not seek to deport all immigrants to this country, illegal or not. A registration system is becoming increasingly necessary. While it should be widely understood that not all Muslims are terrorists, rising tensions between American and certain Muslim-based terrorist cells should be a call for some sort of precautions.
A registration system will keep Americans safe from potential terrorists, because it is important to know who is coming into the country. The Syrian refugees that are coming have very little information tied to them. Many are not women and children. Rather, they are young men who want to live in better places. Tracking them is important for safety.
Registering American Muslims will not fight Islamic extremism, it will only open the floodgates to other acts of discrimination and perhaps even lead to more terrorism. Say we create a registry system for Muslims in America, what happens next? Next time there's a mass shooting or bombing and ISIS claims responsibility, what are they going to do? Round up every Muslim in America? Japanese internment all over again. And what if they make the registration available to the public? Muslims will be treated like sex offenders. ISIS and other Islamic fundamentalist groups are looking for excuses to claim the West is Islamophobic, and a registry system in America will give them just that.
Information has the power to protect and oppress. I do not agree with regulating Muslims in a similar fashion to how the Jews were in Germany or the Japanese in American during World War 2. I believe that the list would most likely be used by extremists groups to target Muslims who will then retaliate.
However, I do agree with being cautious and submitting people from certain risk-adverse regions to advanced immigration screenings.
P.S: note how I said "Region" not "Religion"?
I think that any plans for a Muslim registration system will be worse than ineffective in deterring terrorism - on the contrary I believe that such a system would cause more domestic terrorism. If radical groups are able to claim this is Western intolerance the groups will then become more attractive to impressionable people.
Trump's plans to require Muslims to register themselves, a plan he discussed at length on the campaign trail, would not help keep America safe. If anything, it would exacerbate our current issues with terrorist threats because those Muslims that are inclined to radical, violent acts would feel even more incentive to do so, under the impression that they and their religion are being unfairly targeted. For those Muslims that are everyday citizens and have no affiliation with terrorist groups, such a registration system would only make their lives - especially travel plans - more difficult, and make them more likely to be subjected to harassment.